Landweber Iterative Regularization Method for Identifying the Initial Value Problem of the Rayleigh–Stokes Equation

One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.

show abstract

Updating the Landweber Iteration Method for Solving Inverse Problems

Al-Mahdawi

Alkattan

Abotaleb

et al. 2022

Mathematics

View full text Add to dashboard Cite

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).

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Landweber Iterative Regularization Method for Identifying the Initial Value Problem of the Rayleigh–Stokes Equation

Cited by 3 publications

References 37 publications

Three regularization methods for identifying the initial value of time fractional advection–dispersion equation

Three regularization methods for identifying the initial value of time fractional advection–dispersion equation

Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

Updating the Landweber Iteration Method for Solving Inverse Problems

Contact Info

Product

Resources

About