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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
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Abstract: We introduce and analyze a stable procedure for the approximation of $\langle f^\dagger, \varphi\rangle $ where $f^\dagger$ is the least residual norm solution of the minimal norm of the ill-posed equation $Af=g$, with compact operator $A:X\to Y$ between Hilbert spaces, and $\varphi\in X$ has some smoothness assumption. Our method is based on a finite number of singular values of $A$ 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 $\varphi$.

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Additional Information

M. T. Nair
Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

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

Received by editor(s): December 10, 2003
Published electronically: August 26, 2004
Article copyright: © Copyright 2004 American Mathematical Society