A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations

P. Jidesh, Vorkady S. Shubha and Santhosh George

Applied Mathematics and Computation, 2015, vol. 254, issue C, 148-156

Abstract: George and Elmahdy (2012), considered an iterative method which converges quadratically to the unique solution xαδ of the method of Lavrentiev regularization, i.e., F(x)+α(x-x0)=yδ, approximating the solution xˆ of the ill-posed problem F(x)=y where F:D(F)⊆X⟶X is a nonlinear monotone operator defined on a real Hilbert space X. The convergence analysis of the method was based on a majorizing sequence. In this paper we are concerned with the problem of expanding the applicability of the method considered by George and Elmahdy (2012) by weakening the restrictive conditions imposed on the radius of the convergence ball and also by weakening the popular Lipschitz-type hypotheses considered in earlier studies such as George and Elmahdy (2012), Mahale and Nair (2009), Mathe and Perverzev (2003), Nair and Ravishankar (2008), Semenova (2010) and Tautanhahn (2002). We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining order optimal error estimate. In the concluding section the method is applied to numerical solution of the inverse gravimetry problem.

Keywords: Iterative method; Quadratic convergence; Nonlinear ill-posed equations; Lavrentiev regularization; Adaptive method (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314017512
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:254:y:2015:i:c:p:148-156

DOI: 10.1016/j.amc.2014.12.090

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().