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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A finite dimensional realization of the mollifier method for compact operator equations
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by M. T. Nair and Shine Lal PDF
Math. Comp. 74 (2005), 1281-1290 Request permission

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
  • Email: mtnair@iitm.ac.in
  • Shine Lal
  • Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
  • Email: lalshine@hotmail.com
  • Received by editor(s): December 10, 2003
  • Published electronically: August 26, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1281-1290
  • MSC (2000): Primary 65J10; Secondary 65R10
  • DOI: https://doi.org/10.1090/S0025-5718-04-01707-7
  • MathSciNet review: 2137003