Computation of Functions of Triangular Matrices.

Abstract

A simple relation exists among the elements of phi(T) when phi is an analytic function and T is triangular. This permits the rapid build up of phi(T) from its diagonal. An analogous relation holds for block triangular matrices. This permits the formation in real arithmetic of real functions of real matrices with complex eigenvalues. The confluent case is included. Algorithms are given some numerical examples.