Influence of the order between discretization and regularization in solving ill-posed problems

被引：0

作者：

Grammont, Laurence ^{[1
]}

Vasconcelos, Paulo B. ^{[2
,3
]}

机构：

[1] Univ Jean Monnet, Univ Claude Bernard Lyon 1, Ecole Cent Lyon, ICJ UMR5208,CNRS,INSA Lyon, F-69622 St Etienne, France

[2] Univ Porto, Ctr Matemat, Porto, Portugal

[3] Univ Porto, Fac Econ, Porto, Portugal

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2025年 / 230卷

关键词：

Fredholm integral equations; Inverse problems; Ill-posed problems; Tikhonov regularization; Projection; Computational methods; FREDHOLM INTEGRAL-EQUATIONS;

D O I：

10.1016/j.matcom.2024.02.010

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Discretization and regularization are required steps to provide a stable approximation when solving integral equations of the first kind. The integral operator involved may be approximated by a sequence of finite rank operators and then the regularization procedure is applied. On the other hand, a regularization procedure can be conceived prior to the discretization. Both approaches are developed, implemented and compared for certain projection based methods.

引用

页码：400 / 412

页数：13

共 7 条

[1]

Engl H.W., 1996, MATH ITS APPL

[2] CONVERGENCE ANALYSIS OF A REGULARIZED DEGENERATE KERNEL-METHOD FOR FREDHOLM INTEGRAL-EQUATIONS OF THE 1ST KIND [J].