LDU FACTORIZATION OF NONSINGULAR TOTALLY NONPOSITIVE MATRICES

被引：16

作者：

Canto, Rafael ^{[1
]}

Koev, Plamen ^{[2
]}

Ricarte, Beatriz ^{[1
]}

Urbano, Ana M. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46071 Valencia, Spain

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2008年 / 30卷 / 02期

关键词：

nonsingular matrix; totally nonpositive matrix; LDU factorization;

D O I：

10.1137/060662897

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An n x n real matrix A is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix A, with a(11) < 0 in terms of its LDU factorization (L(U)) is a unit lower- (upper-) triangular matrix, respectively, and D is a diagonal matrix). This characterization allows us to significantly reduce the number of minors to be checked in order to decide the total nonpositivity of a nonsingular matrix with a negative ( 1, 1) entry.

引用

页码：777 / 782

页数：6

共 12 条

[1] TOTALLY POSITIVE MATRICES [J].

ANDO, T .

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

[2]

[Anonymous], 1996, MATH APPL

[3]

[Anonymous], 2000, ELECTRON J LINEAR AL

[4]

Cryer C. W., 1973, Linear Algebra and Its Applications, V7, P83, DOI 10.1016/0024-3795(73)90039-6

[5]

Fallat S., 2000, ELECTRON J LINEAR AL, V7, P1

[6] Compressions of totally positive matrices [J].

Fallat, SM ;

Herman, A ;

Gekhtman, MI ;

Johnson, CR .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2006, 28 (01) :68-80

[7]

Gasca M, 1996, MATH APPL, V359, P109

[8] TOTAL POSITIVITY AND NEVILLE ELIMINATION [J].

GASCA, M ;

PENA, JM .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 165 :25-44

[9] TOTAL POSITIVITY, QR FACTORIZATION, AND NEVILLE ELIMINATION [J].

GASCA, M ;

PENA, JM .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1993, 14 (04) :1132-1140

[10]

GASCA M, 1994, LINEAR ALGEBRA APPL, V198, P133

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