A finite dimensional realization of the mollifier method for compact operator equations

Authors:
M. T. Nair and Shine Lal

Journal:
Math. Comp. **74** (2005), 1281-1290

MSC (2000):
Primary 65J10; Secondary 65R10

Published electronically:
August 26, 2004

MathSciNet review:
2137003

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce and analyze a stable procedure for the approximation of where is the least residual norm solution of the minimal norm of the ill-posed equation , with compact operator between Hilbert spaces, and has some smoothness assumption. Our method is based on a finite number of singular values of and some finite rank operators. Our results are in a more general setting than the one considered by Rieder and Schuster (2000) and Nair and Lal (2003) with special reference to the mollifier method, and it is also applicable under fewer smoothness assumptions on .

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Additional Information

**M. T. Nair**

Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Email:
mtnair@iitm.ac.in

**Shine Lal**

Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Email:
lalshine@hotmail.com

DOI:
https://doi.org/10.1090/S0025-5718-04-01707-7

Received by editor(s):
December 10, 2003

Published electronically:
August 26, 2004

Article copyright:
© Copyright 2004
American Mathematical Society