Angelova, V.; Petkov, P. Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix. Applied Sciences 2024, 14, 1417, doi:10.3390/app14041417.
Angelova, V.; Petkov, P. Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix. Applied Sciences 2024, 14, 1417, doi:10.3390/app14041417.
Angelova, V.; Petkov, P. Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix. Applied Sciences 2024, 14, 1417, doi:10.3390/app14041417.
Angelova, V.; Petkov, P. Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix. Applied Sciences 2024, 14, 1417, doi:10.3390/app14041417.
Abstract
A rigorous perturbation analysis of the singular value decomposition
of a real matrix of full column rank is presented. It is shown that the
SVD perturbation problem is well posed only in case of distinct singular values.
The analysis involves the solution of coupled systems of linear equations and
produces asymptotic (local) componentwise perturbation bounds of the entries of
the orthogonal matrices participating in the decomposition of the given matrix
and of its singular values. Local bounds are derived for the
sensitivity of the singular subspaces measured by the angles between the
unperturbed and perturbed subspaces. An iterative scheme is described to find
global bounds on the respective perturbations. The analysis implements the same
methodology used previously to determine componentwise perturbation bounds of
the Schur form and the QR decomposition of a matrix.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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