Structured perturbation analysis of sparse matrix pencils with s-specified eigenpairs

We study the structured backward error analysis of s-specified (1≤s≤n)eigenpairs of n-by-n matrix pencils. The structures we consider include, T-symmetric, T-skew-symmetric, Hermitian, skew-Hermitian, T-even, T-odd, H-even, H-odd, T-palindromic, T-anti-palindromic, H-palindromic, and H-anti-palindro...

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Bibliographic Details
Published in:Linear algebra and its applications 2020-10, Vol.602, p.93-119
Main Authors: Ahmad, Sk. Safique, Kanhya, Prince
Format: Article
Language:English
Subjects:
Backward error of eigenpairs
Error analysis
Generalized eigenvalue problem
Linear algebra
Mathematical analysis
Matrix methods
Pencils
Perturbation methods
Perturbation theory
Sparse matrices
Sparsity
Structured matrix pencils
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Summary:We study the structured backward error analysis of s-specified (1≤s≤n)eigenpairs of n-by-n matrix pencils. The structures we consider include, T-symmetric, T-skew-symmetric, Hermitian, skew-Hermitian, T-even, T-odd, H-even, H-odd, T-palindromic, T-anti-palindromic, H-palindromic, and H-anti-palindromic matrix pencils. Minimal structured perturbations are constructed with respect to Frobenius norm such that s-specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil which preserves sparsity.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.04.030