IJPAM: Volume 5, No. 2 (2003)

ON THE RITZ METHOD AND ITS GENERALIZATION
FOR ILL-POSED EQUATIONS
WITH NON-SELFADJOINT OPERATORS

M. Thamban Nair$^1$, Eberhard Schock$^2$
$^1$Department of Mathematics
Indian Institute of Technology Madras
Chennai-600 036, INDIA
e-mail: mtnair@iitm.ac.in
$^2$Department of Mathematics
Iniversity of Kaiserslautern
67653 Kaiserslautern, GERMANY
e-mail: schock@mathematik.uni-kl.de


Abstract.Lavrent'ev's method or simplified regularization for an ill-posed operator equation $Tx=y$ is usually applied when $T$ is a positive selfadjoint operator. We modify this procedure to suit for a general bounded operator $T$ by considering $\vert T\vert$ which results in an apparent Ritz method, and also consider its generalization to obtain better convergence rates using a priori and a posteriori parameter choice strategies.

Received: February 19, 2002

AMS Subject Classification: 65J20, 35R30, 45L10

Key Words and Phrases: Tikhonov regularization, Ritz method, apparent Ritz method, discrepancy principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 2