Title: Accurate and verified numerical computation of the matrix determinant

Authors: Takeshi Ogita

Addresses: Division of Mathematical Sciences, School of Arts and Sciences, Tokyo Woman’s Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

Abstract: This paper is concerned with the numerical computation of the determinant of matrices. An algorithm for rigorously enclosing the determinant of a matrix is proposed, especially for extremely ill-conditioned cases. To achieve it, an accurate algorithm for inverse LU factorisation is used. Then accurate and verified results of the determinant can be efficiently obtained for a wide range of problems. An algorithm for computing the exact value of the determinant of an integer matrix is also proposed. Numerical results are presented showing the performance of the proposed algorithms.

Keywords: matrix determinant; verified numerical computation; accurate numerical algorithm; ill-conditioned matrices; verification.

DOI: 10.1504/IJRS.2012.044287

International Journal of Reliability and Safety, 2012 Vol.6 No.1/2/3, pp.242 - 254

Received: 25 Nov 2010
Accepted: 26 Jan 2011
Published online: 27 Dec 2014 *

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