三对角矩阵和单对角矩阵以及两个单对角矩阵的逆和

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-06-21 DOI:10.1016/j.laa.2024.06.018

Sébastien Bossu

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引用次数: 0

摘要

将两个单对数矩阵之和作为下三角、三对角和上三角矩阵的乘积，建立了一种新的因式分解，从而得出了三对角矩阵反演的半封闭形式公式。随后的因式分解被建立起来，从而得出两个单对矩阵逆和的半封闭形式公式。介绍了推导特定革兰氏矩阵符号逆的应用，并研究了公式的数值稳定性。

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Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied.

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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.