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Finite dimensional realization of mollifier methods: a new stable approach. (English) Zbl 1076.65049

The authors consider an ill-posed operator equation \(Af=g\), where \(A: X \to Y\) is a bounded operator between Hilbert spaces \(X\) and \(Y\), and \(X=X(\Omega)\) is a space of functions on an open set \(\Omega \subset \mathbb{R}^k\). A new finite dimensional procedure for the recently developed method of mollifiers is suggested. An application to the problem of 2D-tomography is analyzed.

MSC:

65J10 Numerical solutions to equations with linear operators
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47A52 Linear operators and ill-posed problems, regularization
92C55 Biomedical imaging and signal processing
65R10 Numerical methods for integral transforms
44A12 Radon transform
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References:

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[11] DOI: 10.1137/S0036142998347619 · Zbl 0961.65112 · doi:10.1137/S0036142998347619
[12] DOI: 10.1090/S0025-5718-03-01526-6 · Zbl 1022.65066 · doi:10.1090/S0025-5718-03-01526-6
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