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AIMS Mathematics

2025, Volume 10, Issue 2: 2854-2868. doi: 10.3934/math.2025133
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The shift-based scaling and recursing algorithm for evaluating the action of the matrix $ \varphi $-functions

  • School of Mathematics, Changchun Normal University, 677 Changji North Road, Changchun, MO 130032, China
  • Received: 09 November 2024 Revised: 21 January 2025 Accepted: 05 February 2025 Published: 17 February 2025

  • MSC : 65L05, 65F10, 65F30

  • In this paper, we present an efficient method for computing the action of matrix $ \varphi $-functions. Our approach is based on a scaling and recursing procedure and incorporates a shifting technique as a preprocessing step to enhance efficiency. We conduct a forward error analysis to determine the optimal scaling parameter and polynomial degree for achieving the desired accuracy. Numerical comparisons with existing algorithms demonstrate that the proposed algorithm performs well in terms of both accuracy and efficiency.

    Citation: Xianan Lu, Dongping Li, Zhixin Zhao. The shift-based scaling and recursing algorithm for evaluating the action of the matrix $ \varphi $-functions[J]. AIMS Mathematics, 2025, 10(2): 2854-2868. doi: 10.3934/math.2025133

    Related Papers:

  • In this paper, we present an efficient method for computing the action of matrix $ \varphi $-functions. Our approach is based on a scaling and recursing procedure and incorporates a shifting technique as a preprocessing step to enhance efficiency. We conduct a forward error analysis to determine the optimal scaling parameter and polynomial degree for achieving the desired accuracy. Numerical comparisons with existing algorithms demonstrate that the proposed algorithm performs well in terms of both accuracy and efficiency.



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