There are some limitations in the null test measurement in the stitching interferometry. In order to meet the null test conditions, the moving distance between the sub-apertures often deviates from the theoretical preset distance, which leads to a position deviation of sub-apertures under measurements. To overcome this problem, an algorithm for data processing is proposed. We used iterative calculation of the deviations between the sub-apertures to adjust their positions, to ensure the local validity of the linear approximation algorithm and realize the exact stitching. A cylindrical lens as an object for experimental examination of the proposed method was taken. The obtained results demonstrate the validity, reliability and feasibility of our iterative stitching algorithm.

This paper presents a new adaptive and optimal algorithm for the trajectory tracking control of a quadrotor using iterative learning algorithm (ILA) and enumerative learning algorithm. Ordinarily the ILA, as an adaptive method, can perform well with PID control to improve the controller’s performance for a nonlinear system. Quadrotors are considered as non-linear and unstable systems which the use of an adaptive and optimal controller can increase its stability and decrease error level. In this method, a PID controller is proposed for the outer and inner control loops of a quadrotor and the ILA is used to adapt PID control gains. Subsequently, an enumerative learning algorithm is used to optimize the learning rates of the ILA. For this purpose, at first, the dynamic model of the quadrotor is acquired. After that, the structure of the inner and outer control loops is defined. In the end, the simulation results for the trajectory tracking control of a quadrotor are demonstrated. Through simulation, it is concluded that as time increases, the performance of the suggested control method in trajectory tracking control becomes better and better and error signals convergence to zero.

The node position information is critical in the wireless sensor network (WSN). However, the existing positioning algorithms commonly have low positioning accuracy because of noise interferences in communication. To solve this problem, this paper presents an iterative positioning model based on distance correction to improve the positioning accuracy of the target node in WSN. First, the log-distance distribution model of received signal strength indication (RSSI) ranging is built and the noise impact factor is derived based on the model. Second, the initial position coordinates of the target node are obtained based on the triangle centroid localization algorithm, thereby calculating the distance deviation coefficient under the influence of noise. Then, the ratio of the distance measured by the log-normal distribution model to the median distance deviation coefficient is taken as the new distance between the anchor node and the target node. Based on the new distance, the triangular centroid positioning algorithm is used again to calculate the target node coordinates. Finally, the iterative positioning model is constructed, and the distance deviation coefficient is updated repeatedly to update the positioning result until the set number of iterations is reached. Experiment results show that the proposed iterative positioning model can improve positioning accuracy effectively.

Recently, a layer-stacked ESN model named deep echo state Network (DeepESN) has been established. As an interactional model of recurrent neural network and deep neural network, investigations of DeepESN are of significant importance in both areas. Optimizing the structure of neural networks remains a common task in artificial neural networks, and the question of how many neurons should be used in each layer of DeepESN must be stressed. In this paper, our aim is to solve the problem of choosing the optimized size of DeepESN. Inspired by the sensitive iterative pruning algorithm, a neuronal similarity-based iterative pruning merging algorithm (NS-IPMA) is proposed to iteratively prune or merge the most similar neurons in DeepESN. Two chaotic time series prediction tasks are applied to demonstrate the effectiveness of NS-IPMA. The results show that the DeepESN pruned by NS-IPMA outperforms unpruned DeepESN with the same network size, and NS-IPMA is a feasible and superior approach to improving the generalization performance of DeepESN.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover’s algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we develop a distributed application with a key-value data structure based on Grover’s algorithm called IQuCS . Consider a database with duplicates. By encoding each element to a binary type with a unique key and forming a key-value pair, we can count the number of occurrences of each element in the database based on quantum computing. We have optimized the operation process by filtering data points to make it more efficient. To determine the effect of this optimization, we evaluate it with datasets of different sizes and with different numbers of duplicates. With the assistance of classical computers, IQuCS can reduce the problem set for each query. Due to this reduction, IQuCS requires fewer qubits. Through the iterative management, IQuCS achieves a reduction of qubit virtualized consumption, up to 66.2%, with reasonable accuracy.

In this paper, it is proved that s-iteration with error and Picard-Mann iteration with error iterative processes converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive map. This convergence is almost -stable and -stable. Applications of these results to the operator equations, where is a strongly accretive and accretive mappings of into itself.

The properties of iterative splitting methods with serial versions have been analyzed since recent years, see [1] and [3]. We extend the iterative splitting methods to a class of parallel versions, which allow to reduce the computational time and keep the benet of the higher accuracy with each iterative step. Parallel splitting methods are nowadays important to solve large problems, which can be splitted in subproblems and computed independently with the dierent processors. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, see [2], [10] and [15]. Such a exibilisation with multisplitting methods allow to decompose large iterative splitting methods and recover the benet of their underlying waveform-relaxation (WR) methods. We discuss the convergence results of the parallel iterative splitting methods, while we could reformulate such an error to a summation of the individual WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods and present dierent numerical applications to validate the benet of the parallel versions.

In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a simple two-step iteration. This approach significantly improves the convergence and requires no surd numbers in computation of the arctangent function.

Koala (Phascolarctos cinereus) is an iconic folivorous marsupial native to the sclerophyll forests and woodlands of Australia. Due to the ever-changing habitat, this species is highly vulnerable to anthropogenic factors such as habitat loss and fragmentation, and this is reflected in the increasing number of injured and/or diseased koalas over the years. The majority of adult koalas admitted at wildlife hospitals are deceased, either due to natural causes, or have to be euthanized. Thus, orphaned koala joeys constitute a substantial number of wildlife rescues, and mortality is also prevalent in koala joeys being hand-reared/rehabilitated, with little knowledge about the causes of such high rates of mortality. Wildlife hospitals/rehabilitation centres are inherently stressful, and although the hypothalamic–pituitary–adrenal (HPA) axis plays a vital role in mediating the stress endocrine function (by producing glucocorticoids such as cortisol), there are no studies quantifying glucocorticoids in koala joeys. To contribute to this dearth of research, we sampled a total of seven individuals residing at Port Macquarie Koala Hospital and noted their clinical information. Faecal samples were collected from all seven koala joeys during routine cage cleaning. In total, 123 faecal samples were collected, processed and analysed for cortisol using enzyme-immunoassay (EIA). We used the iterative baseline approach to determine baseline and peak concentrations of FCM in koala joeys. Baseline concentrations ranged between 14.11 ng/g – 51.10 ng/g (healthy – sick), whereas, peak FCM concentrations ranged between 25.65 ng/g – 56.58 ng/g (healthy – sick). There was a significant difference (p < 0.05) between FCM concentrations of healthy and impaired individuals. Healthy individuals displayed relatively consistent FCM concentrations, whereas, diseased individuals displayed a significant increase in FCM concentrations over time. Our study provides the first record of baseline and peak FCM concentrations in rescued koala joeys with their associated clinical condition. Future studies can use the iterative baseline approach to determine FCM concentration in wild koala joeys that can serve as a baseline to compare glucocorticoid levels of rescued joeys.

In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. Using this procedure, we achieve a remarkable increase in the order of convergence, raising it from p to p + 3 units, which results in a remarkable improvement in the overall performance. We have conducted comprehensive numerical tests in various scenarios to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes.

In addition to provide an extremely clean environment for primary loop of high-temperature gas-cooled reactor (HTR), the primary helium circulator (PHC) using electromagnetic levitation technology also provides an effective means for vibration control. Besides synchronous vibration produced by mass imbalance and sensor runout, double-frequency vibration produced by unbalanced magnetic pull (UMP) is serious in PHC engineering prototype (PHC-EP). In this paper, we firstly analyzed the mechanism of UMP and the multi-frequency vibration characteristics in combination with the PHC-EP. Then we put forward a distributed iterative learning control (ILC) algorithm and a parallel control scheme to suppress the periodic vibrations. Finally, we verified the methods by carrying out experimental researches on the active magnetic bearing (AMB) bench of PHC-EP. The results show that the methods put forward in this paper have significant control effect on the double-frequency vibration generated by UMP of the PHC-EP, and provide theoretical and practical references for the PHC safe operation in HTR.

This paper presents a novel dynamic camera parameter control method for position and posture estimation of highly miniaturized AR markers (micro AR markers) using a low cost general camera. The proposed method performs iterative calculation of the marker’s position and posture to converge them to specified accuracy with dynamically updating the camera’s zoom, focus and other parameter values based on the detected marker’s depth distances. For a 10 mm square micro AR marker, the proposed system demonstrated recognition accuracy of better than ±1.0% for depth distance and 2.5∘ for posture angle with a maximum recognition range of 1.0 m. In addition, the iterative calculation time was at most 0.7 seconds in an initial detection of the marker. These experimental results suggest that the proposed method and system can be applied to a robotic precise handling of small objects with low cost.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

This article addresses the trajectory tracking between two non-identical systems with chaotic properties. We employ the Rossler chaotic and RCL-shunted Josephson junctions model in similar phase space to study trajectory tracking. In order to achieve the goal tracking, we afford two stages to approximate the target tracking. The first stage utilizes the active control technique to transfer the output signal from the RCLs-J system into the quasi-Rossler system. Then next, the RCLs-J system employs the proposed the iterative learning control scheme and the control signal from the drive system to trace the trajectory of Rossler system. The numerical results demonstrate the proposed method and the tracking system is asymptotically stable.

The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article.

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.

The research presented in this paper concerns the determination of the attraction basins of the Newton’s iterative method which was used to solve the non-linear systems of observational equations associated with the geodetic measurements. The authors considered simple observation systems corresponding to the intersections, or linear and angular resections, used in practice. The main goal was to investigate the properties of the sets of convergent in the initial points of the applied iterative method. An important issue regarding the possibility of automatic and quick selection of such points was also considered. Therefore, the answers to the questions regarding the geometric structure of the basins, their limitations, connectedness or self-similarity were sought. The research also concerned the iterative structures of the basins, i.e. maps of the number of iterations which are necessary to achieve the convergence of the Newton’s method. The determined basins were compared with the areas of convergence that result from theorems on the convergence of the Newton’s method, i.e. the conditions imposed on the eigenvalues and norms of the matrices of the studied iterative systems. One of the essential results of the research is the indication that the obtained basins of attraction contain areas resulting from the theoretical premises and their diameters can be comparable with the sizes of the analyzed geodetic structures. Consequently, in the analyzed cases it is possible to construct methods that enable quick selection of the initial starting points or automation of such selection. The paper also characterizes the global convergence mechanism of the Newton’s method for disconnected basins and, as a consequence, the non-local initial points, i.e. located far from the solution points.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

This research not only dedicated a less restrictive method of iteration-varying function for a learning control law to design a controller but also synchronize two nonlinear systems with free time-delay. In addition, the mathematical theory of system synchronization has proved rigorously and the theory verified through an example to demonstrate the behavior of each parameter in the theory. The design of a controller using the iterative learning control law is significant for robotic tracking. The controller in this research generates a feed-forward control input using the error dynamics among the drive-response systems. The error dynamics satisfies the Lyapunov function and the combination of output errors, which respectively represented relative estimated differences of the drive-response systems. The iterative learning control rule serves the function of a filter adding previous control error after the end of each iteration. The numerical example of a synchronous system is given a Lorenz system for driving and another with the iterative learning control law for response under different initial condition. The results verify and demonstrate the proposed mathematical theory. The simulation exhibits consistency in the behavior of each parameter to match mathematical theory.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti-6Al-4V grade 5 and ELI. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

Few switching transitions in high power and medium voltage application of Power converters are desirable. The selective harmonics elimination (SHE) pulse width modulation offers a better quality waveform with lower switching transitions and hence lower switching losses. The SHE is a pre-programmed modulation technique where certain amounts of lower order harmonics are removed and fundamental voltage is controlled. After Fourier analysis of output waveform, a set of nonlinear transcendental equations is obtained which exhibits, multiple, unique or no solution in different range of modulation index (MI). In this paper, an iterative method based on the Jacobian estimate is proposed to solve a highly non-linear set of SHE equations. The proposed technique is easy in implementation and can solve a large number of such equations as computation of the Jacobian matrix in the subsequent iteration is estimated from the previous values. Moreover, the proposed method also removes the singularity problem, especially for large SHE equations. High accuracy in the initial guess is also not essential for this method and can converge to the solution with any random initial guess. The computational and simulation results are given to validate the concept. The hardware result is provided to confirm the computational and simulation results.

The accurate of model attitude angel plays an important role on the aerodynamic test results in the wind tunnel test. The original method applies the spherical coordinate system transformation to obtain attitude angel calculation. The model attitude angel is obtained by coordinate transformation and spherical surface mapping applying the nominal attitude angel (the balance attitude angel in the wind tunnel coordinate system) indicated by the mechanism. First, the coordinate transformation of this method is not only complex but also difficult to establish the transformed relationship between the space coordinate systems especially after many steps of coordinate transformation, moreover it cannot realize the iterative calculation of the interference relationship between attitude angels; Second, during the calculate process to solve the problem the arc is approximately used to replace the straight line, the angel for the tangent value, and the inverse trigonometric function is applied. Therefore, in the calculation of attitude angel, the process is complex and inaccurate, which can be solved approximately when calculating small attack angel. However, with the advancing development of modern aerodynamic unsteady research, the aircraft tends to develop high or super large attack angel and unsteady research field. According to engineering practice and vector theory, the concept of vector angel coordinate system is proposed for the first time, and the vector angel coordinate system of attitude angel is established. With the iterative correction calculation and avoiding the problem of approximate and inverse trigonometric function solution, the model attitude calculation process is carried out in detail, which validates that the calculation accuracy and accuracy of model attitude angels are improved. Based on engineering and theoretical methods, a vector angel coordinate system is established for the first time, which gives the transformation and angel definition relations between different flight attitude coordinate systems, that can accurately calculate the attitude angel of the corresponding coordinate system and determine its direction, especially in the channel coupling calculation, the calculation of the attitude angel between the coordinate systems is only related to the angel, and has nothing to do with the change order s of the coordinate system, which simplifies the calculation process.

Tree growth is under the combined influence of abiotic and biotic factors. Trees with different sizes may respond differently to these factors, implying that tree heterogeneity in tree size may also modulate the overall growth trend. To test this hypothesis, we focused on the radial growth trends of natural subalpine forests on the Tibetan Plateau. We first extended the iterative growth model (IGM) to the tree-ring scale (IGMR) to test the applicability of the generalized metabolic growth theory to tree growth. As predicted by the IGMR, the radial growth of trees at the aggregate scale is constrained by a unimodal pattern. Using the IGMR, we reconstructed the historical best growth trajectory (HBGT) of trees within the same community based on the tree with the largest radius and/or longest age in the community. From the average difference between the HBGT and the current radial growth rate of trees with different sizes, we constructed an indicator that can measure the overall variation in tree radial growth. Based on this indicator, we found a negative effect of tree size heterogeneity on the overall variability of tree growth across elevations. Further analysis also revealed that the radial growth rate of trees on the Tibetan Plateau has increased significantly compared to the past, where growing season average temperature and annual minimum temperature were negatively and positively correlated with tree growth below and above the treeline, respectively. Our study not only confirmed that the overall variability of tree growth depends on tree size heterogeneity but also proposed an indicator that reveals net changes in tree radial growth rate relative to the past. These theoretical advances facilitate the understanding of changes in the extent of subalpine forests.

The traditional bored pile technology has some arduous problems, such as the sediment at the pile tip, the mud skin along the pile shaft, and the stress release due to borehole construction. The post-grouted technology at the pile tip of bored pile has emerged because of demand. The grouting migration height (GMH) is of great significance to the strengthen and reinforcement of the pile foundation. This paper derives the calculation formula of the GMH based on the theory of the column hole expansion and Herschel-Bulkley model. The influence of relevant parameters on the GMH is discussed. Aiming at the problem of the grouting migration along the pile shaft in layered soils, the iterative calculation method of the GMH is proposed. The correctness of the GMH is verified by an engineering case, which can guide the engineering practice. The result shows that the GMH increases with the increase of the grouting pressure, the pile diameter and the thickness of the mud skin, and the grouting pressure is positively correlated with the GMH. The GMH decreases with the increase of the buried depth, the consistency coefficient and the rheological index. On this basis, the correctness of the GMH is verified by an engineering case.

As time progresses and technology improves, biological data sets are continuously increasing in size. New methods and new implementations of existing methods are needed to keep pace with this increase. In this paper, we present a high performance computing(HPC)-capable implementation of Iterative Random Forest (iRF). This new implementation enables the explainable-AI eQTL analysis of SNP sets with over a million SNPs. Using this implementation we also present a new method, iRF Leave One Out Prediction (iRF-LOOP), for the creation of Predictive Expression Networks on the order of 40,000 genes or more. We compare the new implementation of iRF with the previous R version and analyze its time to completion on two of the world's fastest supercomputers Summit and Titan. We also show iRF-LOOP's ability to capture biologically significant results when creating Predictive Expression Networks. This new implementation of iRF will enable the analysis of biological data sets at scales that were previously not possible.

This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ; λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Compliant amplifying mechanisms are used widely in high-precision instruments driven by piezoelectric actuators, and the dynamic and static characteristics of these mechanisms are closely related to instrument performance. Although the majority of existing research has focused on analysis of their static characteristics, the dynamic characteristics of the mechanisms affect their response speeds directly. Therefore, this paper proposes a comprehensive theoretical model of compliant amplifying mechanisms based on the multi-body system transfer matrix method to analyze the dynamic and static characteristics of these mechanisms. The effects of the main amplifying mechanism parameters on the displacement amplification ratio and the resonance frequency are analyzed comprehensively using the control variable method. An iterative optimization algorithm is also used to obtain specific parameters that meet the design requirements. Finally, simulation analyses and experimental verification tests are performed. The results indicate the feasibility of using the proposed theoretical compliant amplifying mechanism model to describe the mechanism’s dynamic and static characteristics, which represents a significant contribution to the design and optimization of compliant amplifying mechanisms.

Through the use of machine learning algorithms like the Support Vector Machine, it has been show that burn extent can be accurately mapped from hyperspatial drone imagery in both grasslands and forests. Despite these successes, hyperspatial imagery must be acquired via drones, requiring large amounts of time and resources to capture areas much smaller than the large catastrophic fires which result in the majority of the lands burned each year by wildland fires. To overcome this difficulty, high spatial resolution satellite imagery from Worldview2 can be substituted for hyperspatial drone imagery, allowing for larger regions of images to be acquired more easily and efficiently. Additionally, Worldview2 trades spatial resolution for spectral resolution and extent, capturing images in 8 multispectral bands as opposed to 3 band imagery in the visible spectra. This research examines the utility of each of the 8 bands observed in Worldview2 imagery using an Iterative Dichotomiser 3 decision tree, then uses these bands to map burn extent and biomass consumption. Several classifications of burn extent and biomass consumption are produced and compared based on the bands used as inputs. The results show that using Worldview2 imagery to map burn extent and biomass consumption results in highly accurate maps, with slight improvements when additional bands are added.

In this article we present a SCILAB implementation of algebraic iterative reconstruction methods for discretisation of inverse problems in imaging. These so-called row action methods rely on semi-convergence for achieving the necessary regularisation of the problem. We implement this method using SCILAB and provide a few simplified test problems: medical tomography, seismic tomography and walnut tomography.Numerical results show the capability of this method for the original and perturbed right-hand side vector.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ; . It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

In this work the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions we arrive at the following fourth-order differential equation

Crop type and field boundary mapping enable cost-efficient crop management on the field scale and serve as the basis for yield forecasts. Our study uses a data set with crop types and corresponding field borders from the federal state of Bavaria, Germany, as documented by farmers from 2016 to 2018. The study classified corn, winter wheat, barley, sugar beet, potato, and rapeseed as the main crops grown in Upper Bavaria. Corresponding Sentinel-2 data sets include the normalised difference vegetation index (NDVI) and raw band data from 2016 to 2018 for each selected field. The influences of clouds, raw bands, and NDVI on crop type classification are analysed, and the classification algorithms, i.e., support vector machine (SVM) and random forest (RF), are compared. Field boundary detection and extraction are based on non-iterative clustering and a newly developed procedure based on Canny edge detection. The results emphasise the application of Sentinel’s raw bands (B1–B12) and RF, which outperforms SVM with an accuracy of up to 94%. Furthermore, we forecast data for an unknown year, which slightly reduces the classification accuracy. The results demonstrate the usefulness of the proof-of-concept and its readiness for use in real applications.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

This work addresses the problem of automatic head pose estimation and its application in 3D gaze estimation using low quality RGB--D sensors without any subject cooperation or manual intervention. The previous works on 3D head pose estimation using RGB--D sensors require either an offline step for supervised learning or 3D head model construction which may require manual intervention or subject cooperation for complete head model reconstruction. In this paper, we propose a 3D pose estimator based on low quality depth data, which is not limited by any of the aforementioned steps. Instead, the proposed technique relies on modeling the subject's face in 3--D rather than the complete head, which in turn, relaxes all of the constraints with the previous works. The proposed method is robust, highly accurate and fully automatic. Moreover, it does not need any offline step. Unlike some of the previous works, the method only uses depth data for pose estimation. The experimental results on the Biwi head pose database confirm the efficiency of our algorithm in handling large pose variations and partial occlusion. We also evaluate the performance of our algorithm on IDIAP database for 3D head pose and eye gaze estimation.

Empirical Colebrook equation from 1939 is still accepted as an informal standard to calculate friction factor during the turbulent flow (4000 < Re < 10⁸) through pipes from smooth with almost negligible relative roughness (ε/D→0) to the very rough (up to ε/D = 0.05) inner surface. The Colebrook equation contains flow friction factor λ in implicit logarithmic form where it is, aside of itself; λ, a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D; λ = f (λ, Re, ε/D). To evaluate the error introduced by many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate value of the friction factor λ from the Colebrook equation as accurate as possible. The most accurate way to achieve that is using some kind of iterative methods. Usually classical approach also known as simple fixed point method requires up to 8 iterations to achieve the high level of accuracy, but does not require derivatives of the Colebrook function as here presented accelerated Householder’s approach (3^rd order, 2^nd order: Halley’s and Schröder’s method and 1^st order: Newton-Raphson) which needs only 3 to 7 iteration and three-point iterative methods which needs only 1 to 4 iteration to achieve the same high level of accuracy. Strategies how to find derivatives of the Colebrook function in symbolic form, how to avoid use of the derivatives (Secant method) and how to choose optimal starting point for the iterative procedure are shown. Householder’s approach to the Colebrook’s equations expressed through the Lambert W-function is also analyzed. One approximation to the Colebrook equation based on the analysis from the paper with the error of no more than 0.0617% is shown.

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of linear programming problem. The optimal path refers to a path of minimum length according to the Euclidean metric. The apex method is based on the predictor-corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. Also, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

We present a MATLAB-based, open source reconstruction software for Hybrid Imaging problem arising from Current Density Impedance Imaging (CDII) and Acoustic-Electrical Impedance Tomography (AEIT), utilizing mixed finite element method solver of Darcy toolbox {\tt DarcyLite}~. For a formulation of hybrid inverse problems in impedance tomography the successive substitution iterative schemes are adapted and an reconstruction algorithm is developed. The problem formulation is a class of hybrid imaging modality which is current density impedance imaging or Acoustic-Electrical Impedance Tomography. The proposed algorithm is implemented numerically in two dimensions.

There are two reasons to have an efficient algorithm for identifying all maximal Lyndon substrings of a string: firstly, Bannai et al. introduced in 2015 a linear algorithm to compute all runs of a string that relies on knowing all maximal Lyndon substrings of the input string, and secondly, Franek et al. showed in 2017 a linear equivalence of sorting suffixes and sorting maximal Lyndon substrings of a string, inspired by a novel suffix sorting algorithm of Baier. In 2016, Franek et al. presented a brief overview of algorithms for computing the Lyndon array that encodes the knowledge of maximal Lyndon substrings of the input string. Among the presented were two well-known algorithms for computing the Lyndon array: a quadratic in-place algorithm based on iterated Duval's algorithm for Lyndon factorization, and a linear algorithmic scheme based on linear suffix sorting, computing inverse suffix array, and applying to it the Next Smaller Value algorithm. Duval's algorithm works for strings over any ordered alphabet, while for linear suffix sorting, a constant or an integer alphabet is required. The authors at that time were not aware of Baier's algorithm. In 2017, our research group proposed a novel algorithm for the Lyndon array. Though the proposed algorithm is linear in the average case and has O(n log(n)) worst-case complexity, it is interesting as it emulates the fast Fourier algorithm's recursive approach and introduces tau-reduction that might be of independent interest. In 2018, we presented a linear algorithm to compute the Lyndon array of a string inspired by Phase I of Baier's algorithm for suffix sorting. This paper presents theoretical analysis of these two algorithms and provides empirical comparisons of both their C++ implementations with respect to iterated Duval's algorithm.

To keep the global navigation satellite system functional during extreme conditions, it is a trend to employ autonomous navigation technology with inter-satellite link. As in the newly built BeiDou system (BDS-3) equipped with Ka-band inter-satellite links, every individual satellite has the ability of communicating and measuring distances among each other. The system also has less dependence on the ground stations and improved navigation performance. Because of the huge amount of measurement data, centralized data processing algorithm for orbit determination is suggested to be replaced by a distributed one in which each satellite in the constellation is required to finish a partial computation task. In current paper, the balanced extended Kalman filter algorithm for distributed orbit determination is proposed and compared with whole-constellation centralized extended Kalman filter, iterative cascade extended Kalman filter, and increasing measurement covariance extended Kalman filter. The proposed method demands a lower computation power however yields results with a relatively good accuracy.