COMPUTING THE LOGARITHM OF A SYMMETRICAL 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 t he original matrix to a tridiagonal matrix by orthogonal similarity tr ansformations and applying Pade approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments ind icate that the method is quite efficient when the matrix is not very i ll-conditioned. (C) 1998 IMACS/Elsevier Science B.V.