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Numerical differentiation by a Fourier extension method with super-order regularization

Author

Listed:
  • Chen, Baoqin
  • Zhao, Zhenyu
  • Li, Zhi
  • Meng, Zehong

Abstract

Based on the idea of Fourier extension, we develop a new method for numerical differentiation. The Tikhonov regularization method with a super-order penalty term is presented to deal with the illposdness of the problem and the regularization parameter can be chosen by a discrepancy principle. For various smooth conditions, the solution process of the new method is uniform and order optimal error bounds can be obtained. Numerical experiments are also presented to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Chen, Baoqin & Zhao, Zhenyu & Li, Zhi & Meng, Zehong, 2018. "Numerical differentiation by a Fourier extension method with super-order regularization," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 1-10.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:1-10
    DOI: 10.1016/j.amc.2018.04.005
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    Cited by:

    1. Zhao, Zhenyu & You, Lei, 2021. "A numerical differentiation method based on legendre expansion with super order Tikhonov regularization," Applied Mathematics and Computation, Elsevier, vol. 393(C).

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