A new constructive root bound for algebraic expressions

Chen Li, Chee Yap

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

Abstract

Computing effective root bounds for constant algebraic expressions is a critical problem in the Exact Geometric Computation approach to robust geometric programs. Classical root bounds are often nonconstructive. Recently, various authors have proposed bounding methods which might be called constructive root bounds. For the important class of radical expressions, Burnikel et al (BFMS) have provided a constructive root bound which, in the division-free case, is an improvement over previously known bounds and is essentially tight. In the presence of division, their bound reguires a guadratic blowup in root bit-bound compared to the division-free case. We present a new constructive root bound that avoids this guadratic blowup and which is applicable to a more general class of algebraic expressions. This leads to dramatically better performance in some computations. We also give an improved version of the degree-measure bound from Mignotte and BFMS. We describe our implementation in the context of the Core Library, and report on some experimental results.

Original languageEnglish (US)
Title of host publicationProceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages496-505
Number of pages10
StatePublished - 2001
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: Apr 30 2001May 1 2001

Other

Other2001 Operating Section Proceedings, American Gas Association
CountryUnited States
CityDallas, TX
Period4/30/015/1/01

Fingerprint

Roots
Division
Blow-up
Exact Geometric Computation
Computing
Experimental Results

Keywords

  • Algorithms
  • Design
  • Experimentation
  • Measurement
  • Performance
  • Theory
  • Verification

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Li, C., & Yap, C. (2001). A new constructive root bound for algebraic expressions. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 496-505)

A new constructive root bound for algebraic expressions. / Li, Chen; Yap, Chee.

Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. p. 496-505.

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

Li, C & Yap, C 2001, A new constructive root bound for algebraic expressions. in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 496-505, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.
Li C, Yap C. A new constructive root bound for algebraic expressions. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. p. 496-505
Li, Chen ; Yap, Chee. / A new constructive root bound for algebraic expressions. Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. pp. 496-505
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