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

• Articles • Previous Articles     Next Articles

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

LIU Jian-Jun1,2, HE Guo-Qiang1, KANG Chuan-Gang1,3   

  1. 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

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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

2010 MSC Number: 

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