In Praise of numerical computation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 suchf activities.

Original languageEnglish (US)
Title of host publicationEfficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday
Pages380-407
Number of pages28
Volume5760 LNCS
DOIs
StatePublished - 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5760 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Fingerprint

Numerical Computation
Computational geometry
Computer science
Numerical analysis
Numerical models
Iteration
Computational Science
Computing
Models of Computation
Computational Techniques
Algorithm Design
Computational Geometry
Approximation
Applied mathematics
Subdivision
Numerical Analysis
Pathway
Computer Science
Continuum
Synthesis

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Yap, C. (2009). In Praise of numerical computation. In Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday (Vol. 5760 LNCS, pp. 380-407). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5760 LNCS). https://doi.org/10.1007/978-3-642-03456-5_26

In Praise of numerical computation. / Yap, Chee.

Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday. Vol. 5760 LNCS 2009. p. 380-407 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5760 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yap, C 2009, In Praise of numerical computation. in Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday. vol. 5760 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5760 LNCS, pp. 380-407. https://doi.org/10.1007/978-3-642-03456-5_26
Yap C. In Praise of numerical computation. In Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday. Vol. 5760 LNCS. 2009. p. 380-407. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-03456-5_26
Yap, Chee. / In Praise of numerical computation. Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday. Vol. 5760 LNCS 2009. pp. 380-407 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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