Homeier-like methods for regularization of nonlinear ill-posed equations in Hilbert space
Document Type
Article
Publication Title
Partial Differential Equations in Applied Mathematics
Abstract
Homeier-like methods have been extensively studied in the literature for solving non-linear operator equation of the form F(x)=y in the Banach or Hilbert space setting. Motivated by the work of George et al. (2023), we extend some class of Homeier-like methods to approximate ill-posed operator equation in Hilbert space. Two Homeier-like iterative schemes are proposed for approximating the nonlinear ill-posed operator equation F(x)=y in Hilbert space, where F is monotone. Lavrentiev regularization method and recurrence relation are employed for convergence analysis. The regularization parameter is chosen by apriori parameter choice strategy with new source condition as studied by George et al. (2023). We also supply a numerical example for comparison study of the proposed method with some of the Lavrentiev regularization methods in the literature.
DOI
10.1016/j.padiff.2023.100569
Publication Date
12-1-2023
Recommended Citation
P.B., Suma and Erappa, Shobha M., "Homeier-like methods for regularization of nonlinear ill-posed equations in Hilbert space" (2023). Open Access archive. 7527.
https://impressions.manipal.edu/open-access-archive/7527
