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Bounds for variable degree rational L∞ approximations to the matrix exponential

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  • Tsitouras, Ch.
  • Famelis, I.Th.

Abstract

In this work we derive new alternatives for efficient computation of the matrix exponential which is useful when solving Linear Initial Value Problems, vibratory systems or after semidiscretization of PDEs. We focus especially on the two classes of normal and nonnegative matrices and we present intervals of applications for rational L∞ approximations of various degrees for these types of matrices in the lines of [7, 8]. Our method relies on Remez algorithm for rational approximation while the innovation here is the choice of the starting set of non-symmetrical Chebyshev points. Only one Remez iteration is then usually enough to quickly approach the actual L∞ approximant.

Suggested Citation

  • Tsitouras, Ch. & Famelis, I.Th., 2018. "Bounds for variable degree rational L∞ approximations to the matrix exponential," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 376-386.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:376-386
    DOI: 10.1016/j.amc.2018.06.040
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    References listed on IDEAS

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    1. D. F. Papadopoulos & T. E. Simos, 2013. "The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, May.
    2. T. E. Simos, 2012. "Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, April.
    3. T. E. Simos, 2012. "New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, May.
    4. Junyan Ma & T. E. Simos, 2016. "Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(05), pages 1-20, May.
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