An efficient method for approximating products of functions of matrices with vectors

Given an n x n symmetric positive definite matrix A and a vector c, numerical methods for approximating A1/mc, e^Ac, and ln(A)c are developed, analyzed, and computationally tested. Each method applies Gragg's method with Richardson extrapolation to numerically solve specific initial-value problems to approximate A1/mc, e^Ac, and ln(A)c. Reduction of A to tridiagonal form is first performed to increase the efficiency of the method.