HADAMARD FUNCTIONS OF INVERSE M-MATRICES

被引：11

作者：

Dellacherie, Claude ^{[1
]}

Martinez, Servet ^{[2
,3
]}

San Martin, Jaime ^{[2
,3
]}

机构：

[1] Univ Rouen, UMR 6085, Lab Raphael Salem, F-76821 Mont St Aignan, France

[2] Univ Chile, CNRS, UMI 2807, Ctr Math Modelling, Santiago, Chile

[3] Univ Chile, CNRS, UMI 2807, Dept Engn Math, Santiago, Chile

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2009年 / 31卷 / 02期

关键词：

M-matrices; Hadamard functions; ultrametric matrices; potential matrices; GENERALIZED ULTRAMETRIC MATRICES; PRESERVE;

D O I：

10.1137/060651082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the class of generalized ultrametric matrices (GUM) is the largest class of bipotential matrices stable under Hadamard increasing functions. We also show that any power alpha >= 1, in the sense of Hadamard functions, of an inverse M- matrix is also inverse M- matrix. This was conjectured for alpha = 2 by Neumann in [Linear Algebra Appl., 285 (1998), pp. 277-290], and solved for integer alpha >= 1 by Chen in [Linear Algebra Appl., 381 (2004), pp. 53-60]. We study the class of filtered matrices, which include naturally the GUM matrices, and present some sufficient conditions for a filtered matrix to be a bipotential.

引用

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页码：289 / 315

页数：27

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