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Nonlinear implicit iterative method for solving nonlinear ill-posed problems

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Jian-jun Liu  (柳建军), Guo-qiang He  (贺国强) & Chuan-gang Kang  (康传刚)

  2. PetroChina Pipeline R&D Center, Langfang, 065000, Hebei Province, P. R. China

    Jian-jun Liu  (柳建军)

  3. Shandong University of Finance, Jinan, 250014, P. R. China

    Chuan-gang Kang  (康传刚)

Authors
  1. Jian-jun Liu  (柳建军)
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  2. Guo-qiang He  (贺国强)
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  3. Chuan-gang Kang  (康传刚)
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Corresponding author

Correspondence to Guo-qiang He  (贺国强).

Additional information

Communicated by Xing-ming GUO

Project supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104) and the Shanghai Leading Academic Discipline Project (No. J50101)

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Liu, Jj., He, Gq. & Kang, Cg. Nonlinear implicit iterative method for solving nonlinear ill-posed problems. Appl. Math. Mech.-Engl. Ed. 30, 1183–1192 (2009). https://doi.org/10.1007/s10483-009-0913-1

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  • DOI: https://doi.org/10.1007/s10483-009-0913-1

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Chinese Library Classification

2000 Mathematics Subject Classification

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