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Numerical differentiation by radial basis functions approximation

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Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation. Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

    T. Wei

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    T. Wei & Y. C. Hon

Authors
  1. T. Wei
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  2. Y. C. Hon
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Correspondence to T. Wei.

Additional information

Communicated by Joe Ward

*The work described in this paper was partially supported by a grant from CityU (Project No. 7001646) and partially supported by the National Natural Science Foundation of China (No. 10571079).

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Wei, T., Hon, Y.C. Numerical differentiation by radial basis functions approximation. Adv Comput Math 27, 247–272 (2007). https://doi.org/10.1007/s10444-005-9001-0

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  • DOI: https://doi.org/10.1007/s10444-005-9001-0

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