An isospectral transformation between Hessenberg–bidiagonal matrix pencils and Hessenberg matrices without using subtraction

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-02 DOI:10.1016/j.laa.2025.04.022

Katsuki Kobayashi , Kazuki Maeda , Satoshi Tsujimoto

引用次数: 0

Abstract

We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type.

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黑森伯格双对角矩阵铅笔和黑森伯格矩阵之间的等谱变换，不使用减法

利用正交多项式理论，将上下双对角矩阵的矩阵铅笔化广义特征值问题转化为保持稀疏性的标准特征值问题，提出了一种保持特征值的变换算法。该过程没有减法，减法会导致数值不稳定。进一步讨论了上双对角矩阵为Hessenberg型的扩展情况下的算法。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.