Approximation of the determinant of large sparse symmetric positive   definite matrices
  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. 
Arnold Reusken