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In Praise of Numerical Computation

  • Chapter
Efficient Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5760))

Abstract

Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.

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Authors
  1. Chee K. Yap
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Editors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Georges-Köhler-Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Institut für Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Helmut Alt

  3. Fachbereich IV - Informatik, Universität Trier, 54286, Trier, Germany

    Stefan Näher

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Yap, C.K. (2009). In Praise of Numerical Computation. In: Albers, S., Alt, H., Näher, S. (eds) Efficient Algorithms. Lecture Notes in Computer Science, vol 5760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03456-5_26

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  • DOI: https://doi.org/10.1007/978-3-642-03456-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03455-8

  • Online ISBN: 978-3-642-03456-5

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