An implicit Landweber method for nonlinear ill-posed operator equations

• Autores: Wei Wang, Bo Han
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 2, 2009, págs. 607-613
• Idioma: inglés
• DOI: 10.1016/j.cam.2008.12.016
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• Resumen

  • In this paper, we are interested in the solution of nonlinear inverse problems of the form F(x)=y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. We conclude with numerical examples confirming the theoretical results, including comparisons with the classical Landweber iteration and presented modified Landweber methods.