Componentwise and normwise perturbation analysis for the anti-triangular Schur decomposition

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.cam.2025.117092

Jia Yan Wu , Xiao Shan Chen , Hai–Wei Sun

引用次数: 0

Abstract

This paper presents componentwise and new normwise perturbation bounds for the anti-triangular Schur decomposition of a square matrix. In particular, we derive sensitivity estimates and condition numbers of eigenvalues and

Z

-isotropic subspaces and improve the normwise condition number of such decomposition given by Chen, Li and Ng [SIAM J. Matrix Anal., 33(2012): 325–335]. Numerical examples are given to test the obtained bounds.

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反三角Schur分解的分量和正态摄动分析

本文给出了方阵反三角Schur分解的分量摄动界和新的正态摄动界。特别地，我们导出了特征值和z各向同性子空间的敏感性估计和条件数，并改进了Chen， Li和Ng给出的这种分解的正态条件数[SIAM J. Matrix Anal]。农业学报，33(2012):325-335。最后给出了数值例子来验证所得到的边界。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.