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Boosting the computation of the matrix exponential

Author

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  • Sastre, J.
  • Ibáñez, J.
  • Defez, E.

Abstract

This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Padé algorithm for the computation of the matrix exponential, providing higher accuracy and cost performances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:206-220
    DOI: 10.1016/j.amc.2018.08.017
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Javier Ibáñez & José M. Alonso & Jorge Sastre & Emilio Defez & Pedro Alonso-Jordá, 2021. "Advances in the Approximation of the Matrix Hyperbolic Tangent," Mathematics, MDPI, vol. 9(11), pages 1-20, May.
    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.
    3. Bader, Philipp & Blanes, Sergio & Casas, Fernando & Seydaoğlu, Muaz, 2022. "An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 383-400.
    4. Javier Ibáñez & Jorge Sastre & Pedro Ruiz & José M. Alonso & Emilio Defez, 2021. "An Improved Taylor Algorithm for Computing the Matrix Logarithm," Mathematics, MDPI, vol. 9(17), pages 1-19, August.

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    1. 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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