Principal minors, Part II: The principal minor assignment problem

被引：25

作者：

Griffin, Kent ^{[1
]}

Tsatsomeros, Michael J. ^{[1
]}

机构：

[1] Washington State Univ, Dept Math, Pullman, WA 99164 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 419卷 / 01期

关键词：

principal submatrix; inverse eigenvalue problem; Schur complement;

D O I：

10.1016/j.laa.2006.04.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The inverse problem of finding a matrix with prescribed principal minors is considered. A condition that implies a constructive algorithm for solving this problem will always succeed is presented. The algorithm is based on reconstructing matrices from their principal submatrices and Schur complements in a recursive manner. Consequences regarding the overdeterminancy of this inverse problem are examined, leading to a faster (polynomial time) version of the algorithmic construction. Care is given in the MATLAB (R) implementation of the algorithms regarding numerical stability and accuracy. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：125 / 171

页数：47

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