New Hermite series expansion for computing the matrix cosine (in Press and online), E. Defez, J. Ibañez, J. Peinado, P. Alonso-Jordá and J.M. Alonso, Journal of Computational and Applied Mathematics, Volume 408, July 2022, 114084, https://doi.org/10.1016/j.cam.2022.114084

# Author: Jesús Peinado

## Accurate approximation of the hyperbolic matrix cosine using Bernouilli matrix Polynomials

Accurate approximation of the hyperbolic matrix cosine using Bernouilli matrix Polynomials, E. Defez, J. Ibáñez, J.M. Alonso, J.Peinado and J. Sastre, in the International Conference Mathematical Modeling in Engineering & Human Behaviour 2021, Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, July, 14-16, 2021, Valencia (Spain)

## On Bernouilli matrix polynomials and matrix exponential approximation

On Bernouilli matrix polynomials and matrix exponential approximation (in Press and online), E. Defez, J. Ibañez, P. Alonso-Jordá, J.M. Alonso, J. Peinado, Journal of Computational and Applied Mathematics.Volume 404, April 2022, 113207, https://doi.org 10.1016/j.cam.2020.113207

## Computing Matrix Trigonometric Functions with GPU through Matlab

Computing Matrix Trigonometric Functions with GPUs through Matlab, P. Alonso, J. Peinado, J. Ibañez, J. Sastre, E. Defez, The Journal of Supercomputing, 75, 2019, 1227–1240 , doi: https://doi.org/10.1007/s11227-018-2354-1, Preprint

## On the inverse of the Caputo matrix exponential.

On the inverse of the Caputo matrix exponential. (E. Defez, M. Tung, B. Chen-Charpentier and J.M. Alonso) Mathematics (MDPI, ISSN 2227-7390). Vol. 7 (12), 2019, pp. 1137. doi:10.3390/math7121137

## New matrix series expansions for the matrix cosine approximations

New matrix series expansions for the matrix cosine approximations, E. Defez, J. Ibáñez, P. Alonso, J.M. Alonso J. Peinado, and P. Alonso-Jordá, in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2019, Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, July, 10-12, 2019, Valencia (Spain).

## An introduction to the “Group of High Performance Scientific Computing” (HiPerSC)

An introduction to the “Group of High Performance Scientific Computing” (HiPerSC), E. Defez, J. Ibañez, J. Peinado, J. Sastre and M. M. Tung, International Congress on Industrial and Applied Mathematics, ICIAM 2019, July 15th-19th 2019, Valencia (Spain).

## Computing matrix functions by matrix Bernouilli Series

Computing matrix functions by matrix Bernouilli Series, E. Defez, J. Ibañez, J. Peinado, P. Alonso-Jordá and J.M. Alonso, 19th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2019, June-July 2019, Rota (Cadiz)-SPAIN.

## 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, Journal of Computational and Applied Mathematics, vol. 354 pp. 641-650, July 2019 https://doi.org/10.1016/j.cam.2018.12.041, Preprint **Matlab code cosmpol.m**

## 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.