A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems

被引：5

作者：

Pornsawad, Pornsarp ^{[1
,2
]}

Sapsakul, Nantawan ^{[1
,2
]}

Bockmann, Christine ^{[3
]}

机构：

[1] Silpakorn Univ, Fac Sci, Dept Math, 6 Rachamakka Nai Rd, Nakhon Pathom 73000, Thailand

[2] Mahidol Univ, Ctr Excellence Math, Rama 6 Rd, Bangkok 10400, Thailand

[3] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Potsdam, Germany

来源：

MATHEMATICS | 2019年 / 7卷 / 05期

关键词：

nonlinear operator; regularization; discrepancy principle; asymptotic method; optimal rate; LANDWEBER ITERATION;

D O I：

10.3390/math7050419

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the continuous version of modified iterative Runge-Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i. e., the stopping time T is a solution of k F ( x d( T)) y dk = td+ for some d+ > d, and an appropriate source condition. We yield the optimal rate of convergence.

引用

页数：19

共 19 条

[1]

[Anonymous], 2013, NUMERICAL METHODS SO

[2] Iterative Runge-Kutta-type methods for nonlinear ill-posed problems [J].