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A Newton type iterative method for heat-conduction inverse problems

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Abstract

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.

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References

  1. Bech J V, Blackwell B, Clair C St Jr. Inverse heat conduction: ill-posed problems[M]. New York: Wiley, 1985.

    Google Scholar 

  2. Groetsch C W. Inverse problems in the mathematical sciences[M]. Braunschweig: Vieweg, 1993.

    Google Scholar 

  3. Engl H, Hanke M, Neubauer A. Regularization of inverse problems[M]. Dordrecht: Kluwer, 1996.

    Google Scholar 

  4. He Guoqiang, Chen Y M. An inverse problem for the Burgers’ equation[J]. Journal of Computational Mathematics, 1999, 11(2):275–284.

    Google Scholar 

  5. Hansen P C. Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAM Review, 1992, 34(4):561–580.

    Article  MATH  MathSciNet  Google Scholar 

  6. Bakushiskii A B. The problems of the convergence of the iteratively regularized Gauss-Newton method[J]. Comput Maths Math Phys, 1992, 32(9):1353–1359.

    Google Scholar 

  7. Kaltenbacher B. A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems[J]. Numerical Mathematics, 1998, 79(4):501–528.

    Article  MATH  MathSciNet  Google Scholar 

  8. Bauer F, Hohage T. A Lepskij-type stopping rule for regularized Newton methods[J]. Inverse Problems, 2005, 21(6):1975–1991.

    Article  MATH  MathSciNet  Google Scholar 

  9. He Guoqiang, Liu Linxian. A kind of implicit iterative methods for ill-posed operator equations[J]. Journal of Computational Mathematics, 1999, 17(3):275–284.

    MATH  MathSciNet  Google Scholar 

  10. He Guoqiang, Wang Xinge, Liu Linxian. Implicit iterative methods with variable control parameters for ill-posed operator equations[J]. Acta Mathematica Scientia B, 2000, 20(4):485–494.

    MATH  MathSciNet  Google Scholar 

  11. Groetsch C W. The theory of Tikhonov regularization for Fredholm equations of the first kind[M]. Boston: Pitman, 1984.

    Google Scholar 

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Authors and Affiliations

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

    He Guo-qiang  (贺国强) (Professor) & Meng Ze-hong  (孟泽红)

Authors
  1. He Guo-qiang  (贺国强)
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  2. Meng Ze-hong  (孟泽红)
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Corresponding author

Correspondence to He Guo-qiang  (贺国强).

Additional information

Communicated by LU Chuan-jing

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He, Gq., Meng, Zh. A Newton type iterative method for heat-conduction inverse problems. Appl Math Mech 28, 531–539 (2007). https://doi.org/10.1007/s10483-007-0414-y

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  • DOI: https://doi.org/10.1007/s10483-007-0414-y

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Chinese Library Classification

2000 Mathematics Subject Classification

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