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.
P. Nadukandi and N. J. Higham, "Computing the Wave-Kernel Matrix Functions", Manchester Institute for the Mathematical Sciences, MIMS EPrint 2018.4, 2018.
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.
git clone https://github.com/nadukandi/wkm.git
cd wkm