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

被引：1

作者：

Bossu, Sebastien ^{[1
]}

机构：

[1] UNC Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 699卷

关键词：

Tridiagonal matrix; Single-pair matrix; Semiseparable matrix; Inverse matrix; Gram matrix; Covariance matrix; Continuant sequence; QR method;

D O I：

10.1016/j.laa.2024.06.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：129 / 158

页数：30

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