Nonlinear implicit iterative method for solving nonlinear ill-posed problems

doi:10.1007/s10483-009-0913-1

Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1183-1192.doi: https://doi.org/10.1007/s10483-009-0913-1

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

柳建军^1,2 贺国强¹ 康传刚^1,3

1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. PetroChina Pipeline R&D Center, Langfang 065000, Hebei Province, P. R. China;
3. Shandong University of Finance, Jinan 250014, P. R. China

收稿日期:2008-07-28 修回日期:2009-07-02 出版日期:2009-09-01 发布日期:2009-09-01

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

LIU Jian-Jun^1,2, HE Guo-Qiang¹, KANG Chuan-Gang^1,3

1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. PetroChina Pipeline R&D Center, Langfang 065000, Hebei Province, P. R. China;
3. Shandong University of Finance, Jinan 250014, P. R. China

Received:2008-07-28 Revised:2009-07-02 Online:2009-09-01 Published:2009-09-01

摘要/Abstract

摘要： In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

关键词: nonlinear ill-posed problem, nonlinear implicit iterative method, monotonicity, convergence

Abstract: In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

Key words: nonlinear ill-posed problem, nonlinear implicit iterative method, monotonicity, convergence

中图分类号:

柳建军贺国强康传刚. Nonlinear implicit iterative method for solving nonlinear ill-posed problems[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(9): 1183-1192.

LIU Jian-Jun;HE Guo-Qiang;KANG Chuan-Gang. Nonlinear implicit iterative method for solving nonlinear ill-posed problems[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(9): 1183-1192.

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

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