# Computing the inertia from sign patterns

Naonori Kakimura, Satoru Iwata

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

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 symmetric matrices. The algorithm runs in O(√nm log n) time for a symmetric matrix of order n with m nonzero entries. In addition, it is shown to be NP-complete to decide whether the inertia of a given symmetric matrix is not determined by its sign pattern.

Original language English 229-244 16 Mathematical Programming 110 1 https://doi.org/10.1007/s10107-006-0056-6 Published - 2007 Jun Yes

### Fingerprint

Sign Pattern
Symmetric matrix
Inertia
Computing
Nonsingular or invertible matrix
Efficient Algorithms
NP-complete problem

### Keywords

• Inertia
• Sign patterns
• Sign-nonsingular symmetric matrices

### ASJC Scopus subject areas

• Software
• Mathematics(all)

### Cite this

Computing the inertia from sign patterns. / Kakimura, Naonori; Iwata, Satoru.

In: Mathematical Programming, Vol. 110, No. 1, 06.2007, p. 229-244.

Research output: Contribution to journalArticle

Kakimura, Naonori ; Iwata, Satoru. / Computing the inertia from sign patterns. In: Mathematical Programming. 2007 ; Vol. 110, No. 1. pp. 229-244.
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