matrices-mp-cosm is a collection of MATLAB functions that generate the selected matrices for testing the matrix cosine in multiprecision. All matrices are square
and have a fixed size. Most of the matrices are taken from the matrix exponential literature, and are real, ill conditioned or rank deficient.
The matrices are used in
Awad H. Al-Mohy, Nicholas J. Higham and Xiaobo Liu. Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. SIAM J. Matrix Anal. Appl., 43(1):233-256, 2022.
The 34 matrices are
% almo2r1 - 2-by-2 matrix by Awad H. Al-Mohy.
% almo2r2 - 2-by-2 matrix by Awad H. Al-Mohy.
% almo4 - 4-by-4 matrix by Awad H. Al-Mohy.
% dahi03 - 4-by-4 matrix from \cite[Ex.~3]{dahi03}.
% dipa00 - 8-by-8 matrix from \cite[Ex.~3.10]{dipa00}.
% edst04 - 20-by-20, log of Cholesky factor of Pascal matrix from \cite{edst04}.
% eigt7 - 7-by-7 matrix from EIGTOOL.
% fahi19 - 10-by-10 matrix from \cite{fahi19}.
% fasi7 - 7-by-7, Massimiliano Fasi's idea from \cite[p. 81]{kags77a}.
% hism03 - 8-by-8 matrix from \cite[expm. 4]{hism03}.
% jemc05r1 - 3-by-3 matrix from \cite[(52)]{jemc05}.
% jemc05r2 - 6-by-6 matrix from \cite[(55)]{jemc05}.
% kase99 - 10-by-10 matrix from \cite[Table 1]{kase99}.
% kela89 - 4-by-4 matrix from \cite[p.~206]{kela89}.
% kela98r1 - 2-by-2 matrix from \cite[Ex.~2]{kela98}.
% kela98r2 - 5-by-5 matrix from \cite[p.~655]{kela98}.
% kela98r3 - 2-by-2 matrix from \cite[Ex.~5]{kela98}.
% kela98r4 - 2-by-2 matrix from \cite[Ex.~3]{kela98}.
% kuda10 - 20-by-20 matrix from \cite{kuda10}.
% lara17r1 - 2-by-2 matrix from \cite[Benchmark #1]{lara17}, \cite[Problem 1]{zhao17}.
% lara17r2 - 3-by-3 matrix from \cite[Benchmark #2]{lara17}, \cite[Problem 2]{zhao17}.
% lara17r3 - 3-by-3 matrix from \cite[Benchmark #3]{lara17}, \cite[Problem 3]{zhao17}.
% lara17r4 - 4-by-4 matrix from \cite[Benchmark #4]{lara17}, \cite[Problem 4]{zhao17}.
% lara17r5 - 12-by-12 matrix from \cite[Benchmark #5]{lara17}, \cite[Problem 5]{zhao17}
% lara17r6 - 8-by-8 matrix from \cite[Benchmark #6]{lara17}, \cite[Problem 6]{zhao17}.
% mopa03r1 - 4-by-4 matrix from \cite{mopa03}.
% mopa03r2 - 3-by-3 matrix from \cite{mopa03}.
% naha95 - 3-by-3 matrix from \cite[p. 370]{naha95}.
% pang85r1 - 6-by-6 matrix from \cite[p.~7, Ex I]{pang85}.
% pang85r2 - 20-by-20 matrix from \cite[p.~9, Ex II]{pang85}.
% pang85r3 - 20-by-20 matrix from \cite[p.~10, Ex III]{pang85}.
% trem05 - 3-by-3 matrix from \cite[(14.17), p. 141]{trem05}.
% ward77r1 - 3-by-3 matrix from \cite{ward77}.
% ward77r2 - 3-by-3 matrix from \cite{ward77}.
Other M-files:
am_properties.m: lists properties of the matrices and is intended for use when this collection is integrated as a group in the Anymatrix collection.
This collection is ready to include as a group in the Anymatrix collection,
for which the name mpcosm should be used.
The codes have been developed under MATLAB 2021a.
See license.txt for licensing information.