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Stable Numerical Differentiation Algorithms Based on the Fourier Transform in Frequency Domain

Author

Listed:
  • Yanling He

    (College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China)

  • Huilin Xu

    (College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China)

  • Xiaoyan Xiang

    (College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China)

Abstract

A class of stable numerical differential algorithms is constructed based on the Fourier transform. The instability of the numerical differentiation problem is overcome by modifying the integral “kernel†in the frequency domain. The convergence of the approximate derivatives is ensured based on some reasonable assumptions of the modified “kernel†function. The a-posteriori choice strategy of the regularization parameter is considered. Moreover, the convergence analysis and error estimate of the approximate derivatives are also given.

Suggested Citation

  • Yanling He & Huilin Xu & Xiaoyan Xiang, 2022. "Stable Numerical Differentiation Algorithms Based on the Fourier Transform in Frequency Domain," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 8(2), pages 34-41, 04-2022.
    • Handle: RePEc:arp:ajoams:2022:p:34-41
    DOI: 10.32861/ajams.82.34.41
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    References listed on IDEAS

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    1. Huilin Xu & Xiaoyan Xiang & Yanling He, 2021. "A Stable Approach for Numerical Differentiation by Local Regularization Method with its Regularization Parameter Selection Strategies," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(1), pages 27-35, 01-2021.
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