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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The approximate inverse in action II: convergence and stability
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by Andreas Rieder and Thomas Schuster PDF
Math. Comp. 72 (2003), 1399-1415 Request permission


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
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  • Thomas Schuster
  • Affiliation: Fachbereich Mathematik, Geb. 36, Universität des Saarlandes, 66041 Saarbrücken, Germany
  • Email:
  • 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:
  • MathSciNet review: 1972743