Computing matrix functions arising in engineering models with orthogonal matrix polynomials. (English) Zbl 1305.65137

Defez, Emilio; Sastre, Jorge; Ibáñez, Javier; Ruiz, Pedro

Math. Comput. Modelling 57, No. 7-8, 1738-1743 (2013).

Summary: Trigonometric matrix functions play a fundamental role in the solution of second order differential equations. Hermite series truncation together with Paterson-Stockmeyer method and the double angle formula technique allow efficient computation of the matrix cosine. A careful error bound analysis of the Hermite approximation is given and a theoretical estimate for the optimal value of its parameters is obtained. Based on the ideas above, an efficient and highly-accurate Hermite algorithm is presented. A MATLAB implementation of this algorithm has also been developed and made available online. This implementation has been compared to other efficient state-of-the-art implementations on a large class of matrices for different dimensions, obtaining higher accuracy and lower computational costs in the majority of cases.

MSC:

65F60	Numerical computation of matrix exponential and similar matrix functions
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Hermite matrix approximation; matrix cosine; MATLAB; error bound

Software:

Matlab; MATLAB expm; mftoolbox; testmatrix