Principal minors, Part I: A method for computing all the principal minors of a matrix

被引：27
|
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; Schur complement; P-matrix; P-problem;
D O I：
10.1016/j.laa.2006.04.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An order O(2(n)) algorithm for computing all the principal minors of an arbitrary n x n complex matrix is motivated and presented, offering an improvement by a factor of n(3) over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a binary order. An implementation of the algorithm in MATLAB (R) is also given and practical considerations are discussed and treated accordingly. (c) 2006 Elsevier Inc. All rights reserved.
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页码：107 / 124
页数：18
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