Exact numerical computation in algebra and geometry

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

Abstract

Many problems in Computational Science & Engineering (CSE) are defined on the continuum. Standard algorithms for these problems are numerical and approximate. Their computational techniques include iteration, subdivision, and approximation. Such techniques are rarely seen in exact or algebraic algorithms. In this tutorial, we discuss a mode of computation called exact numerical computation (ENC) that achieves exactness through numerical approximation. Through ENC, we can naturally incorporate iteration, subdivision and approximation into the design of exact algorithms for computer algebra and computational geometry. Such algorithms are both novel and practical. This tutorial on ENC is divided into three equal parts: (a) Zero Problems (b) Explicitation Problems (c) Techniques and Complexity Analysis of Adaptivity.

Original languageEnglish (US)
Title of host publicationISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
Pages387-388
Number of pages2
DOIs
StatePublished - Dec 1 2009
Event2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of
Duration: Jul 28 2009Jul 31 2009

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Other

Other2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
CountryKorea, Republic of
CitySeoul
Period7/28/097/31/09

    Fingerprint

Keywords

  • Adaptive complexity analysis
  • Exact numerical computation
  • Explicitization problems
  • Numerical algebraic computation
  • Numerical computational geometry
  • Zero bounds

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Yap, C. K. (2009). Exact numerical computation in algebra and geometry. In ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation (pp. 387-388). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1576702.1576757