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.