Approximation of the Determinant of Large Sparse Symmetric Positive Definite Matrices
Arnold Reusken · SIAM Journal on Matrix Analysis and Applications · 2002
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.