Hermite spectral and pseudospectral methods for numerical differentiation

Authors:
Zhenyu Zhao;Junfeng Liu
Affiliations:
College of Science, Guangdong Ocean University, Zhanjiang, 524088, China and School of Mathematical Sciences, Fudan University, Shanghai, 200433, China;Department of Basic Science, Military Transportation University, Tianjin, 300161, China
Venue:
Applied Numerical Mathematics
Year:
2011

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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.