A Scaling and Recovering Algorithm for the Matrix $\varphi$-Functions

This repository contains the algorithm developed in the paper:

A. H. Al-Mohy and X. Liu. A scaling and recovering algorithm for the matrix φ-functions. SIAM J. Sci. Comput., 48(2):A726-A747, 2026.

The main function

The code was tested in MATLAB 2024b.

The main function phi_funm.m computes the phi-functions of a matrix for given indices.

The script simple_test.m runs a simple test. The directory replication/ contains required subroutines for reproducing the results in the paper.

Replicating the results in the paper

To reproduce the results in the paper, the following MATLAB toolboxes need to be installed:

• Advanpix Multiprecision Computing Toolbox

• Anymatrix

where in Anymatrix the test matrix collection

• matrices-expm

needs to be incorporated as a group.

The results presented in the manuscript can be generated by running:

>> run_all_tests

Acknowledgments

This work was supported by the Deanship of Scientific Research at King Khalid University Research Groups Program (grant RGP. 1/318/45).

License

This project is licensed under the terms of the BSD 2-Clause "Simplified" License (SPDX-License-Identifier: BSD-2-Clause).