Working Paper Article Version 1 This version is not peer-reviewed

A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Version 1 : Received: 21 September 2019 / Approved: 22 September 2019 / Online: 22 September 2019 (15:40:27 CEST)

A peer-reviewed article of this Preprint also exists.

Yin, F.; Wu, J.; Song, J.; Yang, J. A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP. Mathematics 2019, 7, 966. Yin, F.; Wu, J.; Song, J.; Yang, J. A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP. Mathematics 2019, 7, 966.

Journal reference: Mathematics 2019, 7, 966
DOI: 10.3390/math7100966

Abstract

In this paper, we proposed a high accurate and stable Legendre transform algorithm which can reduce the potential instability for very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(N(logN)^2/loglogN) in theory and less than O(N(logN)^4) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

Subject Areas

legendre transform; block partitioning; interpolative decomposition; butterfly algorithm

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