Approximation of the determinant of large sparse symmetric positive definite matrices

TL;DR

This paper introduces an efficient method for approximating the determinant of large sparse symmetric positive definite matrices using a sparse approximate inverse, supported by theoretical analysis and numerical experiments.

Contribution

The paper presents a novel approach leveraging sparse approximate inverses for determinant approximation, including error estimation and empirical validation.

Findings

Method achieves accurate approximations efficiently

Theoretical properties support the method's validity

Numerical results demonstrate practical effectiveness

Abstract

This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. 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. A posteriori error estimation techniques are presented. Furthermore, results of numerical experiments are given which illustrate the performance of this new method.