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Two algorithms for computing the matrix cosine function

Author

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  • Sastre, Jorge
  • Ibáñez, Javier
  • Alonso, Pedro
  • Peinado, Jesús
  • Defez, Emilio

Abstract

The computation of matrix trigonometric functions has received remarkable attention in the last decades due to its usefulness in the solution of systems of second order linear differential equations. Several state-of-the-art algorithms have been provided recently for computing these matrix functions. In this work, we present two efficient algorithms based on Taylor series with forward and backward error analysis for computing the matrix cosine. A MATLAB implementation of the algorithms is compared to state-of-the-art algorithms, with excellent performance in both accuracy and cost.

Suggested Citation

  • Sastre, Jorge & Ibáñez, Javier & Alonso, Pedro & Peinado, Jesús & Defez, Emilio, 2017. "Two algorithms for computing the matrix cosine function," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 66-77.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:66-77
    DOI: 10.1016/j.amc.2017.05.019
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    Cited by:

    1. Sastre, J. & Ibáñez, J. & Defez, E., 2019. "Boosting the computation of the matrix exponential," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 206-220.
    2. Jorge Sastre & Javier Ibáñez, 2021. "Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method," Mathematics, MDPI, vol. 9(14), pages 1-23, July.

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