Representation of the exact solution and a stability analysis on the Fredholm integral equation of the first kind in reproducing kernel space

被引：23

作者：

Du, Hong

Cui, Minggen ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Shandong 264209, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[3] Heilongjiang Inst Sci & Technol, Dept Math & Mech, Harbin 150027, Hei Long Jiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 182卷 / 02期

关键词：

Fredholm integral equation; ill-posed problem; reproducing kernel space;

D O I：

10.1016/j.amc.2006.05.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new method is given in order to solve an ill-posed problem on Fredholm integral equation of the first kind. The representation of the exact solution is given and the stability of the solution on Fredholm integral equation of the first kind is discussed in the reproducing kernel space. By the discussions, a conclusion is obtained the stability problem is a well-posed problem in the reproducing kernel space, namely, the measurement errors of the experimental data can not result in unbounded errors of the exact solution. The numerical experiment shows that the new method given in the paper is valid. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1608 / 1614

页数：7

共 11 条

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[2]

Groestch C.W., 1993, INVERSE PROBLEMS MAT

[3]

Hadamard J., 1923, Lectures on the Cauchy Problems in Linear Partial Differential Equations

[4] Size distributions out of static light scattering: Inclusion of distortions from the experimental setup, e.g., a SOFICA-type goniometer [J].