Bounds for the infinity norm of the inverse for certain M- and H-matrices

被引：20

作者：

Kolotilina, L. Yu. ^{[1
]}

机构：

[1] Russian Acad Sci, VA Steklov Math Inst, St Petersburg Branch, St Petersburg 191023, Russia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 2-3期

关键词：

Infinity norm; Inverse matrix; PM-Matrices; PH-Matrices; M-Matrices; H-Matrices; Strictly diagonally dominant matrices;

D O I：

10.1016/j.laa.2008.09.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper presents new two-sided bounds for the infinity norm of the inverse for the so-called PM-matrices, which form a subclass of the class of nonsingular M-matrices and contain the class of strictly diagonally dominant matrices. These bounds are shown to be monotone with respect to the underlying partitioning of the index set, and the equality cases are analyzed. Also an upper bound for the infinity norm of the inverse of a PH-matrix (whose comparison matrix is a PM-nnatrix) is derived. The known Ostrowski, Ahlberg-Nilson-Varah, and Moraca bounds are shown to be special cases of the upper bound obtained. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：692 / 702

页数：11

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