Approximation of the Determinant of Large Sparse Symmetric Positive Definite Matrices

Authors:
Arnold Reusken
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2001

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Abstract

This paper is concerned with the problem of approximating det(A)1/n for a large sparse symmetric positive definite matrix A of order n. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse of A. The method is explained and theoretical properties are discussed. The method is ideal for implementation on a parallel computer. Numerical experiments are described that illustrate the performance of this new method and provide a comparison with Monte Carlo--type methods from the literature.