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The approximate inverse in action II: convergence and stability

Authors: Andreas Rieder and Thomas Schuster
Journal: Math. Comp. 72 (2003), 1399-1415
MSC (2000): Primary 65J10, 65R10
Published electronically: March 26, 2003
MathSciNet review: 1972743
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Abstract: The approximate inverse is a scheme for constructing stable inversion formulas for operator equations. Originally, it is defined on $L^2$-spaces. In the present article we extend the concept of approximate inverse to more general settings which allow us to investigate the discrete version of the approximate inverse which actually underlies numerical computations. Indeed, we show convergence if the discretization parameter tends to zero. Further, we prove stability, that is, we show the regularization property. Finally we apply the results to the filtered backprojection algorithm in 2D-tomography to obtain convergence rates.

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Additional Information

Andreas Rieder
Affiliation: Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung (IWRMM), Universität Karlsruhe, 76128 Karlsruhe, Germany

Thomas Schuster
Affiliation: Fachbereich Mathematik, Geb. 36, Universität des Saarlandes, 66041 Saarbrücken, Germany

Keywords: Approximate inverse, mollification, Radon transform, filtered backprojection
Received by editor(s): September 21, 2001
Published electronically: March 26, 2003
Additional Notes: The second author was supported by Deutsche Forschungsgemeinschaft under grant Lo310/4-1
Article copyright: © Copyright 2003 American Mathematical Society