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Article | REF: AF486 V1

Matrix Functions Computations

Author: Gérard MEURANT

Publication date: October 10, 2014, Review date: April 26, 2021

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2. Methods for calculating f (A)

There are many methods for calculating matrix functions. Some are general, others are designed for specific functions. The most general methods use approximations of the function f and/or factorizations of the matrix A.

Note that a matrix function of a real matrix is not always real. However, if possible, we want to avoid using complex arithmetic if A is real.

Most of the algorithms described below are designed to achieve high accuracy at the lowest possible cost.

2.1 Approximation methods

If we know a Taylor expansion of f in the vicinity of a,

f(x)=
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