Solving engineering models using hyperbolic matrix functions - Defez, Emilio; Sastre, Jorge; Ibáñez, Javier; Peinado, Jesús (Applied mathematical modelling, 2016)
•A method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is presented.•A new error bound analysis is given.•A theoretical estimate for the optimal value of its parameters is obtained.•An efficient and highly-accurate algorithm (implemented in MATLAB) is presented.•A parallel implementation for large scale problems was developed. In this paper a method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is outlined. Hermite series truncation together with Paterson–Stockmeyer method allow to compute the hyperbolic matrix cosine efficiently. A theoretical estimate for the optimal value of its parameters is obtained. An efficient and highly-accurate Hermite algorithm and a MATLAB implementation have been developed. The MATLAB implementation has been compared with the MATLAB function funm on matrices of different dimensions, obtaining lower execution time and higher accuracy in most cases. To do this we used an NVIDIA Tesla K20 GPGPU card, the CUDA environment and MATLAB. With this implementation we get much better performance for large scale problems.