Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (3): 265-275.

• Articles • Previous Articles     Next Articles

 Implicit Iterative Methods Based on Some Orthogonal Polynomials for Ill Posed Operator Equations

 TANG Jian-Guo   

  1. 零陵学院数学系 湖南永州 425006
  • Online:2003-06-25 Published:2003-06-25
  • Supported by:

    湖南省教育厅科研项目(02C355)资助

Abstract:

In this paper, implicit iterative methods (IIMs) based on Chebyshev and Jacobi polynomials for ill posed operator equations are investigated. The relation between IIMs and the explicit iterative methods (EIMs) developed by Hanke is established. An important lemma about residual rational formula of the iterative schemes related to the first and the second Chebyshev polynomials is presented. For nonperturbed and perturbed data, the convergence properties and convergence rate are studied. An implementable algorithm is given by using Moro zov's discrepancy principle, which is a robust regularization algorithm.Finally, numerical examples are also given, which coincide well with theoretical results. 

Key words: Ill posed operator equation, Implicit iterative method; Explicit iterative method, Orthogonal polynomial, Morozovs disrepancy principle

CLC Number: 

  • 65J10
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