On parametrization of totally nonpositive matrices and applications

被引：0

作者：

Huang, Rong ^{[1
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2012年 / 19卷 / 04期

基金：

高等学校博士学科点专项科研基金;

关键词：

totally nonpositive matrices; bidiagonal factorization; accurate computation; NONNEGATIVE MATRICES; ACCURATE; EIGENVALUES; ALGORITHMS; SYSTEMS; SVDS;

D O I：

10.1002/nla.804

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of accurate computations for totally non-negative matrices has been studied; however, it remains open for other sign regular matrices. One major obstacle is that there is no known parametrization of these matrices. The main contribution of the present work is that we provide such parametrization of nonsingular totally nonpositive matrices. A useful application of our results is that these parameters can determine accurately the entries of the inverse of a nonsingular totally nonpositive matrix. Copyright (c) 2011 John Wiley & Sons, Ltd.

引用

页码：742 / 753

页数：12

共 14 条

[1] TOTALLY POSITIVE MATRICES [J].

ANDO, T .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 90 :165-219

[2] The accurate and efficient solution of a totally positive generalized Vandermonde linear system [J].

Demmel, J ;

Koev, P .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2005, 27 (01) :142-152

[3] Computing the singular value decomposition with high relative accuracy [J].

Demmel, J ;

Gu, M ;

Eisenstat, S ;

Slapnicar, I ;

Veselic, K ;

Drmac, Z .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 299 (1-3) :21-80

[4] Accurate SVDs of weakly diagonally dominant M-matrices [J].

Demmel, J ;

Koev, P .

NUMERISCHE MATHEMATIK, 2004, 98 (01) :99-104

[5]

Gasca M, 1996, MATH APPL, V359, P109

[6]

Higham N. J., 2002, Accuracy and stability of numerical algorithms

[7] ERROR ANALYSIS OF THE BJORCK-PEREYRA ALGORITHMS FOR SOLVING VANDERMONDE SYSTEMS [J].

HIGHAM, NJ .

NUMERISCHE MATHEMATIK, 1987, 50 (05) :613-632

[8] Total nonpositivity of nonsingular matrices [J].

Huang, Rong ;

Chu, Delin .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (11) :2931-2941

[9]

Karlin Samuel, 1968, Total Positivity

[10] cAccurate eigenvalues and SVDs of totally nonnegative matrices [J].

Koev, P .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2005, 27 (01) :1-23

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