Fast Taylor polynomial evaluation for the matrix cosine

Fast Taylor polynomial evaluation for the matrix cosine, J. Sastre, J. Ibañez, P. Alonso, J. Peinado and E. Defez, 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018, July 2018, Rota (Cadiz)-SPAIN.

In this work we introduce a new method to compute the matrix cosine. It is based on recent new matrix polynomial evaluation methods for the Taylor approximation and forward and backward error analysis. The matrix polynomial evaluation methods allow to evaluate the Taylor polynomial approximation of the cosine function more efficiently than using Paterson-Stockmeyer method. A MATLAB implementation of the new algorithm is provided, giving better efficiency and accuracy than state-of-the-art algorithms.

 

 

An efficient and accurate algorithm for computing the matrix cosine based on New Hermite approximations

An efficient and accurate algorithm for computing the matrix cosine based on New Hermite approximations, E. Defez, J. Ibáñez, J. Peinado, J. Sastre and P. Alonso, Journal of Computational and Applied Mathematics, Volume 348, pp. 1-13. March 2019. https://doi.org/10.1016/j.cam.2018.08.047, Preprint, Matlab code cosmtayher.m.

In this work we introduce new rational-polynomial Hermite matrix expansions which allow us to obtain a new accurate and efficient method for computing the matrix cosine. This method is compared with other state-of-the-art methods for computing the matrix cosine, including a method based on Padé approximants, showing a far superior efficiency, and higher accuracy. The algorithm implemented on the basis of this method can also be executed either in one or two NVIDIA GPUs, which demonstrates its great computational capacity.

Two algorithms for computing the matrix cosine based on new Hermite approximations