Hermite spectral and pseudospectral methods for numerical differentiation

被引：17
作者：
Zhao, Zhenyu [1 ,2 ]
Liu, Junfeng [3 ]
机构：
[1] Guangdong Ocean Univ, Coll Sci, Zhanjiang 524088, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Mil Transportat Univ, Dept Basic Sci, Tianjin 300161, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2011年 / 61卷 / 12期
基金：
中国博士后科学基金;
关键词：
Ill-posed problem; Numerical differentiation; Hermite spectral method; Regularization; Discrepancy principle; ILL-POSED PROBLEMS; MOLLIFICATION; REGULARIZATION; DERIVATIVES; RECONSTRUCTION;
D O I：
10.1016/j.apnum.2011.09.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1322 / 1330
页数：9
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