Matrix completions and chordal graphs

被引：5

作者：

Harrison, KJ ^{[1
]}

机构：

[1] Murdoch Univ, Perth, WA, Australia

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2003年 / 19卷 / 03期

关键词：

matrix completions; chordal graph;

D O I：

10.1007/s10114-003-0266-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.

引用

页码：577 / 590

页数：14

共 24 条

[11] Numerical ranges and matrix completions [J].

Hadwin, DW ;

Harrison, KJ ;

Ward, JA .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 315 (1-3) :145-154

[12]

Halmos P. R., 1982, GRAD TEXTS MATH, V19

[13]

HARRISON KJ, UNPUB POSITIVE DEFIN

[14]

Helton J.W., 1987, OPERATOR THEORY ANAL, DOI [10.1090/cbms/068, DOI 10.1090/CBMS/068]

[15]

JOHNSON CR, 1991, OPER THEOR, V50, P283

[16] Rank decomposition under combinatorial constraints [J].

Johnson, CR ;

Miller, J .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 251 :97-104

[17] COMPLETION OF PARTIAL MATRICES TO CONTRACTIONS [J].

JOHNSON, CR ;

RODMAN, L .

JOURNAL OF FUNCTIONAL ANALYSIS, 1986, 69 (02) :260-267

[18] UNIQUE MINIMAL RANK EXTENSIONS OF TRIANGULAR OPERATORS [J].

KAASHOEK, MA ;

WOERDEMAN, HJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 131 (02) :501-516

[19]

Kalman R.E., 1979, ACTA POLYTECH SCAND, V31, P9

[20]

LEUKER GS, 1976, SIAM J COMPUT, V5, P266

← 1 2 3 →