Solving Nonlinear Inverse Problems Based on the Regularized Modified Gauss–Newton Method-Reference-Cited by-同舟云学术

Solving Nonlinear Inverse Problems Based on the Regularized Modified Gauss–Newton Method

Published:2022-06 Issue:3 Volume:105 Page:175-177
ISSN:1064-5624
Container-title:Doklady Mathematics
language:en
Short-container-title:Dokl. Math.

Author:

Vasin V. V.

Abstract

Abstract A nonlinear operator equation is investigated in the case when the Hadamard correctness conditions are violated. A two-stage method is proposed for constructing a stable method for solving the equation. It includes modified Tikhonov regularization and a modified iterative Gauss–Newton process for approximating the solution of the regularized equation. The convergence of the iterations and the strong Fejér property of the process are proved. An order optimal estimate for the error of the two-stage method is established in the class of sourcewise representable functions.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1134/S1064562422030103.pdf

Reference8 articles.

1. G. G. Skorik and V. V. Vasin, “Regularized Newton type method for retrieval of heavy water in atmosphere by IR-spectra of the solar light transmission,” Eurasian J. Math. Comput. Appl. 7 (2), 79–88 (2019).

2. V. V. Vasin and G. G. Skorik, “Two-stage method for solving system of nonlinear equations and its applications to the inverse atmosphere sounding problem,” Dokl. Math. 102 (2), 267–270 (2019).

3. V. V. Vasin, Foundations of the Theory of Ill-Posed Problems (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2020) [in Russian].

4. V. V. Vasin and S. Georg, “Expanding the applicability of Tikhonov’s regularization and iterative approximation for ill-posed problems,” J. Inverse Ill-Posed Probl. 22 (4), 593–607 (2014).

5. V. K. Ivanov, “The regularization of linear operator equations of the first kind,” Izv. Vyssh. Uch. Zaved. Mat., No. 10, 50–55 (1967).