On the invertibility of matrices with a double saddle-point structure

被引：0

作者：

Beik, Fatemeh P. A. ^{[1
,3
]}

Greif, Chen ^{[2
]}

Trummer, Manfred ^{[3
]}

机构：

[1] Vali Easr Univ Rafsanjan, Dept Math, POB 518, Rafsanjan, Iran

[2] Univ British Columbia, Dept Comp Sci, Vancouver, BC V6T 1Z4, Canada

[3] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 699卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Matrix inversion; Invertible matrix; Solvability; Double saddle-point systems; Nullity; SCHUR COMPLEMENT; BLOCK PRECONDITIONERS; APPROXIMATION; SYSTEMS; MODEL;

D O I：

10.1016/j.laa.2024.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure that guarantee the unique solvability of double saddle-point systems. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the nullity of the blocks and intersections of their kernels, an explicit formula for the inverse is derived. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

引用

页码：403 / 420

页数：18

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