Thamban Nair M

Department of Mathematics

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

On improving accuracy for Arcangeli's method for solving Ill-posed equations

Integral Equations and Operator Theory

Pereverzev (1995) considered Tikhonov regularization combined with a modified form of a projection method for obtaining stable approximate solutions for ill-posed operator equations. He showed, under a certain a priori choice of the regularization parameter and a specific smoothness assumption on the solution, that the method yields the optimal order with less computational information, in the sense of complexity, than the projection method considered by Plato and Vainikko (1990). In this paper we apply a modified form of the Arcangeli's discrepancy principle for choosing the regularization parameter, and show that the conclusions of Pereverzev still hold. In fact, we do the analysis using a modified form of the generalized Arcangeli's method suggested by Schock (1984) under more flexible smoothness assumption on the solution, as has been done by George and Nair (1998), and derive the optimal result as a special case. Moreover, we compare the computational complexity of the present method with two tradit ional projection methods in the case of a priori parameter choice, and also discuss the computational complexity required to implement the suggested discrepancy principle.

Numerical Functional Analysis and Optimization

Arcangeli's discrepancy principle for a modified projection scheme for ill-posed problems

Journal of Optimization Theory and Applications

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Applicable Analysis

Asymptotic convergence rate of arcangeli's method for III-posed problems

On improving accuracy for Arcangeli's method for solving III-Posed equations

Journal	Integral Equations and Operator Theory
ISSN	0378620X
Open Access	No