The approximate inverse in action II: convergence and stability
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- by Andreas Rieder and Thomas Schuster;
- Math. Comp. 72 (2003), 1399-1415
- DOI: https://doi.org/10.1090/S0025-5718-03-01526-6
- Published electronically: March 26, 2003
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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.References
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Bibliographic Information
- Andreas Rieder
- Affiliation: Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung (IWRMM), Universität Karlsruhe, 76128 Karlsruhe, Germany
- Email: andreas.rieder@math.uni-karlsruhe.de
- Thomas Schuster
- Affiliation: Fachbereich Mathematik, Geb. 36, Universität des Saarlandes, 66041 Saarbrücken, Germany
- Email: thomas.schuster@num.uni-sb.de
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1399-1415
- MSC (2000): Primary 65J10, 65R10
- DOI: https://doi.org/10.1090/S0025-5718-03-01526-6
- MathSciNet review: 1972743