An efficient method for approximating products of functions of matrices with vectors
Martines, Ian Pablo
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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.