Backward error analysis of specified eigenpairs for sparse matrix polynomials

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2022-11-21 DOI:10.1002/nla.2476

Sk. Safique Ahmad, Prince Kanhya

引用次数: 0

Abstract

This article studies the unstructured and structured backward error analysis of specified eigenpairs for matrix polynomials. The structures we discuss include T$$ T $$ ‐symmetric, T$$ T $$ ‐skew‐symmetric, Hermitian, skew Hermitian, T$$ T $$ ‐even, T$$ T $$ ‐odd, H$$ H $$ ‐even, H$$ H $$ ‐odd, T$$ T $$ ‐palindromic, T$$ T $$ ‐anti‐palindromic, H$$ H $$ ‐palindromic, and H$$ H $$ ‐anti‐palindromic matrix polynomials. Minimally structured perturbations are constructed with respect to Frobenius norm such that specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix polynomial that also preserves sparsity. Further, we have used our results to solve various quadratic inverse eigenvalue problems that arise from real‐life applications.

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稀疏矩阵多项式指定特征对的后向误差分析

本文研究了矩阵多项式指定特征对的非结构化和结构化后向误差分析。我们讨论的结构包括T $$ T $$对称、T $$ T $$偏对称、hermite、skew hermite、T $$ T $$偶、T $$ T $$奇、H $$ H $$偶、H $$ H $$奇、T $$ T $$回文、T $$ T $$反回文、H $$ H $$回文和H $$ H $$反回文矩阵多项式。基于Frobenius范数构造了最小结构摄动，使得指定的特征对成为适当摄动的矩阵多项式的精确特征对，并且保持了稀疏性。此外，我们已经使用我们的结果来解决实际应用中出现的各种二次型反特征值问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.