doi:10.3850/978-981-08-5118-7_038

ABSTRACT

This paper is concerned with the numerical computation of the determinant of matrices. Algorithms for computing enclosures and the exact values of the determinant of integer matrices are proposed. The algorithms can treat extremely ill-conditioned matrices. To achieve it, an accurate algorithm for inverse LU factorization is used. Then accurate and verified results of the determinant can efficiently be obtained for much wider range of the problems. A possibility for verifying the singularity of integer matrices is also discussed. Numerical results are also presented showing the performance of the proposed algorithms.

Keywords: Determinant, Verified numerical computation, Verification of singularity.

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