A Newton type iterative method for heat-conduction inverse problems

Applied Mathematics and Mechanics (English Edition)

Volumn 28, Issue 4, 2007, Pages 531-539

  He, Guo Qiang ^a   Meng, Ze Hong ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Implicit iterative method; Inverse problems; Iteration stopping rule; Newton type method; Nonlinear ill posed operator equations

Indexed keywords

HEAT CONDUCTION; LINEARIZATION; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; PROBLEM SOLVING;

IMPLICIT ITERATIVE METHOD; ITERATION STOPPING RULES; NEWTON TYPE METHODS; NONLINEAR ILL-POSED OPERATOR EQUATIONS;

INVERSE PROBLEMS;

EID: 38049187827     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-007-0414-y     Document Type: Article

References (11)

1. Bech J V, Blackwell B, Clair C St Jr. Inverse heat conduction: ill-posed problems[M]. New York: Wiley, 1985.
2. Groetsch C W. Inverse problems in the mathematical sciences[M]. Braunschweig: Vieweg, 1993.
3. Engl H, Hanke M, Neubauer A. Regularization of inverse problems[M]. Dordrecht: Kluwer, 1996.
4. He Guoqiang, Chen Y M. An inverse problem for the Burgers' equation[J]. Journal of Computational Mathematics, 1999, 11(2):275-284.
5. Hansen P C. Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAM Review, 1992, 34(4):561-580.
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.
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.
8. Bauer F, Hohage T. A Lepskij-type stopping rule for regularized Newton methods[J]. Inverse Problems, 2005, 21(6):1975-1991.
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.
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.
11. Groetsch C W. The theory of Tikhonov regularization for Fredholm equations of the first kind[M]. Boston: Pitman, 1984.