Modified version of a simplified Landweber iterative method for nonlinear ill-posed operator equations

Pallavi Mahale () and Ankush Kumar ()
Additional contact information
Pallavi Mahale: Visvesvaraya National Institute of Technology
Ankush Kumar: Visvesvaraya National Institute of Technology

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 241-261

Abstract: Abstract In this paper, we consider a modified version of the simplified Landweber iterative regularization method which require calculation of the Frèchet derivative of the operator F only at the initial guess $$u_0$$ u 0 with step size $$\omega >0$$ ω > 0 for obtaining stable approximate solution of nonlinear ill-posed operator equation of the form $$F(u) = y,$$ F ( u ) = y , where $$F: {\mathcal {D}}(F)\subset U \rightarrow Y$$ F : D ( F ) ⊂ U → Y is nonlinear operator from a Hilbert space U to a Hilbert space Y. We provide convergence analysis for the proposed scheme based on the concept of asymptotic stability. We show convergence of the method and derive error estimate under suitable non-linearity conditions on F. Lastly, the effectiveness of the proffered method is made more visible by showing its applicability to numerical example.

Keywords: Landweber method; Nonlinear ill-posed operator equation; Iterative regularization method; Stopping rule (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00474-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:56:y:2025:i:1:d:10.1007_s13226-023-00474-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-023-00474-3

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().