On the Computation and Perturbation of Matrix Functions

Abstract

For a square complex matrix A and a scalar valued function f(z) defined on the spectrum of A the concept of matrix function is central to the field of matrix analysis and its related application fields. This thesis is concerned with the study and computation of such matrix function. The computation of matrix functions arises naturally when solving matrix equation of the form f(X)=A. In this work, we investigate in particular the matrix equation exp(X)=A. We discuss the solvability as well as computation of solution of this matrix equation, that is logarithms of A. We propose several algorithms to compute matrix logarithm. For each algorithm we provide an error estimate. Finally the sensitivity analysis of •logarithmic function is discussed.