关键词: 不适定算子方程;隐式迭代法;显式迭代法;正交多项式;Morozov残差原则

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