mp-spalg

A multiprecision Schur-Parlett algorithm for computing arbitrary matrix functions without derivatives.

Function include/funm_nd.m is a Schur-Parlett algorithm for computing a function of a square matrix without using derivatives. It evaluates the nontrivial diagonal blocks in the Schur form using randomized approximate diagonalization with a diagonal perturbation.

The function works for an arbitrary function f at a square matrix A and requires only the ability to evaluate f itself; derivatives are not required.

Function test.m runs a simple test of the codes.

Details on the underlying algorithms can be found in the technical report:

N. J. Higham and X. Liu. A Multiprecision Derivative-Free Schur-Parlett Algorithm for Computing Matrix Functions, MIMS EPrint 2020.19, 2020.

All codes used for generating the data in the above report are included in this repository.

Dependencies
The code in this repository requires the Advanpix Multiprecision Computing Toolbox for MATLAB (www.advanpix.com).