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 MathematicsUniversitat Politècnica de València,  July, 14-16, 2021, Valencia (Spain)

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).

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.