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Hermite spectral and pseudospectral methods for numerical differentiation

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
61
Issue
12
Identifiers
DOI: 10.1016/j.apnum.2011.09.006
Keywords
  • Ill-Posed Problem
  • Numerical Differentiation
  • Hermite Spectral Method
  • Regularization
  • Discrepancy Principle

Abstract

Abstract A numerical differentiation problem for a given function with noisy data is discussed in this paper. A mollification method based on spanned by Hermite functions is proposed and the mollification parameter is chosen by a discrepancy principle. The convergence estimates of the derivatives are obtained. To get a practical approach, we also derive corresponding results for pseudospectral (Hermite–Gauss interpolation) approximations. Numerical examples are given to show the efficiency of the method.

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