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
Subtitle of host publicationEssays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday
EditorsSusanne Albers, Helmut Alt, Stefan Naher
Pages380-407
Number of pages28
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)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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