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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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Numerical solution of the ${\mathbb R}$-linear Beltrami equation
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by Marko Huhtanen and Allan Perämäki PDF
Math. Comp. 81 (2012), 387-397 Request permission

Abstract:

The $\mathbb {R}$-linear Beltrami equation appears in applications, such as the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the $\mathbb {R}$-linear Beltrami equation is considered. This gives rise to large and dense $\mathbb {R}$-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are devised. In the numerical experiments, these improvements combined are shown to lead to speed-ups of almost two orders of magnitude in the electrical conductivity problem.
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Additional Information
  • Marko Huhtanen
  • Affiliation: Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • Email: Marko.Huhtanen@tkk.fi
  • Allan Perämäki
  • Affiliation: Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • Email: Allan.Peramaki@tkk.fi
  • Received by editor(s): June 18, 2010
  • Received by editor(s) in revised form: December 15, 2010
  • Published electronically: August 9, 2011
  • Additional Notes: The research of both authors was supported by the Academy of Finland
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 387-397
  • MSC (2010): Primary 65R20, 65F10, 45Q05
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02541-X
  • MathSciNet review: 2833500