Jianjun Liu; Zhe Wang; Guoqiang He; Chuangang Kang

International Journal of Information Technology and Computer Science (IJITCS)

IJITCS Vol. 3, No. 4, 8 Aug. 2011

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Numerical Implementation of Nonlinear Implicit Iterative Method for Solving Ill-posed Problems

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Author(s)

Jianjun Liu ^1,* Zhe Wang ² Guoqiang He ³ Chuangang Kang ⁴

1. PetroChina Pipeline R&D Center, Langfang, P.R.C

2. Research and Innovation Institute Watchdata System Co., Ltd. BeiJing, P.R.C

3. Department of Mathematics, Shanghai University, Shanghai, P.R.C

4. Department of Mathematics, Tianjin Polytechnic University, Tianjin, P.R.C

* Corresponding author.

DOI: https://doi.org/10.5815/ijitcs.2011.04.02

Received: 4 Sep. 2010 / Revised: 12 Jan. 2011 / Accepted: 25 Mar. 2011 / Published: 8 Aug. 2011

Index Terms

Nonlinear, gradient method, regularization, implicit iterative

Abstract

Many nonlinear regularization methods may converge to local minima in numerical implementation for the complexity of nonlinear operator. Under some not very strict assumptions, we implement our proposed nonlinear implicit iterative method and have a global convergence results. Using the convexity property of the modified Tikhonov functional, it combines nonlinear implicit iterative method with a gradient method for solving ill-posed problems. Finally we present two numerical results for integral equation and parameter identification.

Cite This Paper

Jianjun Liu, Zhe Wang, Guoqiang He, Chuangang Kang, "Numerical Implementation of Nonlinear Implicit Iterative Method for Solving Ill-posed Problems", International Journal of Information Technology and Computer Science(IJITCS), vol.3, no.4, pp.9-15, 2011. DOI:10.5815/ijitcs.2011.04.02

Reference

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[4]L. Jianjun, Nonlinear implicit iterative method and regularization GMRES method for solving nonlinear ill-posed problems[D].(in Chinese) Shanghai University, 2008.

[5]M. Hanke, “A Regularizing Levenberg-Marquardt Scheme with Applications to Inverse Ground-water Filtration Problem,”. Inverse Problems. IOP Publlishing. Bristol, vol. 13, pp. 79-95, 1997