Empirical study of an evaluation-based subdivision algorithm for complex root isolation

Narayan Kamath, Irina Voiculescu, Chee Yap

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

Abstract

We provide an empirical study of subdivision algorithms for isolating the simple roots of a polynomial in any desired box region B 0 of the complex plane. One such class of algorithms is based on Newton-like interval methods (Moore, Krawczyk, Hansen-Sengupta). Another class of subdivision algorithms is based on function evaluation. Here, Yakoubsohn discussed a method that is purely based on an exclusion predicate. Recently, Sagraloff and Yap introduced another algorithm of this type, called Ceval. We describe the first implementation of Ceval in Core Library. We compare its performance to the above mentioned algorithms, and also to the well-known MPSolve software from Bini and Florentino. Our results suggest that certified evaluation-based methods such as Ceval are encouraging and deserve further exploration.

Original languageEnglish (US)
Title of host publicationSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Pages155-164
Number of pages10
DOIs
StatePublished - 2011
EventSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - San Jose, CA, United States
Duration: Jun 7 2011Jun 9 2011

Other

OtherSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
CountryUnited States
CitySan Jose, CA
Period6/7/116/9/11

Fingerprint

Subdivision Algorithm
Empirical Study
Isolation
Roots
Evaluation
Root of a polynomial
Newton-like Method
Interval Methods
Evaluation Function
Predicate
Argand diagram
Function evaluation
Software
Polynomials
Class

Keywords

  • Ceval algorithm interval Newton methods
  • Complex root isolation
  • Solving bi-variate systems
  • Subdivision algorithms

ASJC Scopus subject areas

  • Modeling and Simulation

Cite this

Kamath, N., Voiculescu, I., & Yap, C. (2011). Empirical study of an evaluation-based subdivision algorithm for complex root isolation. In SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation (pp. 155-164) https://doi.org/10.1145/2331684.2331710

Empirical study of an evaluation-based subdivision algorithm for complex root isolation. / Kamath, Narayan; Voiculescu, Irina; Yap, Chee.

SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation. 2011. p. 155-164.

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

Kamath, N, Voiculescu, I & Yap, C 2011, Empirical study of an evaluation-based subdivision algorithm for complex root isolation. in SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation. pp. 155-164, SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, San Jose, CA, United States, 6/7/11. https://doi.org/10.1145/2331684.2331710
Kamath N, Voiculescu I, Yap C. Empirical study of an evaluation-based subdivision algorithm for complex root isolation. In SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation. 2011. p. 155-164 https://doi.org/10.1145/2331684.2331710
Kamath, Narayan ; Voiculescu, Irina ; Yap, Chee. / Empirical study of an evaluation-based subdivision algorithm for complex root isolation. SNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation. 2011. pp. 155-164
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