Computing the Wave-Kernel Matrix Functions

About

This repository contains two MATLAB functions to compute (wkm.m) and test (test_wkm.m) the Wave-Kernel Matrix Functions cosh(sqrt(A)) and sinhc(sqrt(A)), where A is any n x n matrix, sinhc(z) = sinh(z)/z for any nonzero scalar z, and sinhc(0) = 1. Details on the underlying algorithms can be found in the MIMS EPrint 2018.4.

The function wkm.m has the following signature.

[C, S] = wkm (A)

where C = cosh(sqrt(A)) and S = sinhc(sqrt(A)). Type help wkm at the MATLAB command prompt for more information.

The function test_wkm.m runs some tests for a suite of matrices chosen from the Matrix Computation Toolbox and the matrix function literature.

test_wkm('mct_testmats');
test_wkm('expm_testmats');
test_wkm('logm_testmats');

Type help test_wkm at the MATLAB command prompt for more information. The Symbolic Math Toolbox (to use variable precision arithmetic) is assumed to be present for the tests. The raw output in the files results_test_wkm.txt and results_multiplier_test_wkm.txt were generated using MATLAB 2017b. The MATLAB script plot_error.m contains the processed data and the code used to generate the figures in the MIMS EPrint 2018.4. The source code of the MATLAB function funm_condest1.m is included in test_wkm.m to compute the condition number estimates of matrix functions. funm_condest1.m is a part of Higham's Matrix Function Toolbox.

Reference

P. Nadukandi and N. J. Higham, "Computing the Wave-Kernel Matrix Functions", Manchester Institute for the Mathematical Sciences, MIMS EPrint 2018.4, 2018.

Funding

Nadukandi was supported by an individual fellowship from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant 702138.
Higham was supported by Engineering and Physical Sciences Research Council grant EP/P020720/1.

Clone this repository

git clone https://github.com/nadukandi/wkm.git
cd wkm