Updating the Landweber Iteration Method for Solving Inverse Problems

Hassan K. Ibrahim Al-Mahdawi, Hussein Alkattan, Mostafa Abotaleb (), Ammar Kadi and El-Sayed M. El-kenawy
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Hassan K. Ibrahim Al-Mahdawi: Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia
Hussein Alkattan: Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia
Mostafa Abotaleb: Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia
Ammar Kadi: Department of Food and Biotechnology, South Ural State University, 454080 Chelyabinsk, Russia
El-Sayed M. El-kenawy: Department of Communications and Electronics, Delta Higher Institute of Engineering and Technology, Mansoura 35111, Egypt

Mathematics, 2022, vol. 10, issue 15, 1-13

Abstract: The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main methods and algorithms to achieve the best results. We considered in this work the linear operator equation and the use of a new version of the Landweber iterative method as an iterative solver. The main goal of updating the Landweber iteration method is to make the iteration process fast and more accurate. We used a polar decomposition to achieve a symmetric positive definite operator instead of an identity operator in the classical Landweber method. We carried out the convergence and other necessary analyses to prove the usability of the new iteration method. The residual method was used as an analysis method to rate the convergence of the iteration. The modified iterative method was compared to the classical Landweber method. A numerical experiment illustrates the effectiveness of this method by applying it to solve the inverse boundary value problem of the heat equation (IBVP).

Keywords: Landweber iteration; ill-posed problem; inverse problem; linear operator equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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