On stable numerical differentiation

被引：114

作者：

Ramm, AG ^{[1
]}

Smirnova, AB ^{[1
]}

机构：

[1] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

MATHEMATICS OF COMPUTATION | 2001年 / 70卷 / 235期

关键词：

numerical differentiation; noisy data; ill-posed problems; multi-point methods; regularization;

D O I：

10.1090/S0025-5718-01-01307-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new approach to the construction of finite-difference methods is presented. It is shown how the multi-point differentiators can generate regularizing algorithms with a stepsize h being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral equation is developed.

引用

页码：1131 / 1153

页数：23

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