Numerical differentiation by radial basis functions approximation

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 unkn...

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Vydáno v:Advances in computational mathematics Ročník 27; číslo 3; s. 247 - 272
Hlavní autoři: Wei, T., Hon, Y. C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: 01.10.2007
Témata:
Approximation
Derivatives
Mathematical analysis
Mathematical models
Numerical differentiation
Radial basis function
Regularization
Strategy
ISSN:1019-7168, 1572-9044
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Shrnutí: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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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-005-9001-0