Computing the inertia from sign patterns

Naonori Kakimura, Satoru Iwata

研究成果: Conference article査読

1 被引用数 (Scopus)

抄録

A symmetric matrix A is said to be sign-nonsingular if every symmetric matrix with the same sign pattern as A is nonsingular. Hall, Li and Wang showed that the inertia of a sign-nonsingular symmetric matrix is determined uniquely by its sign pattern. The purpose of this paper is to present an efficient algorithm for computing the inertia of such matrices. The algorithm runs in O(nm) time for a symmetric matrix of order n with m nonzero entries. The correctness of the algorithm provides an alternative proof of the result by Hall et al. In addition, for a symmetric matrix in general, it is shown to be NP-complete to decide whether the inertia of the matrix is not determined by the sign pattern.

本文言語English
ページ(範囲)236-248
ページ数13
ジャーナルLecture Notes in Computer Science
3509
DOI
出版ステータスPublished - 2005 1 1
外部発表はい
イベント11th International IPCO Conference on Integer Programming and Combinatorial Optimization - Berlin, Germany
継続期間: 2005 6 82005 6 10

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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