Computing the logarithm of a symmetric positive definite matrix

A numerical method for computing the logarithm of a symmetric positive definite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pade approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite efficient when the matrix is not very ill-conditioned. (C) 1998 IMACS/Elsevier Science B.V.