Analytic root clustering: A complete algorithm using soft zero tests

Chee Yap, Michael Sagraloff, Vikram Sharma

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

Abstract

A challenge to current theories of computing in the continua is the proper treatment of the zero test. Such tests are critical for extracting geometric information. Zero tests are expensive and may be uncomputable. So we seek geometric algorithms based on a weak form of such tests, called soft zero tests. Typically, algorithms with such tests can only determine the geometry for "nice" (e.g., non-degenerate, non-singular, smooth, Morse, etc) inputs. Algorithms that avoid such niceness assumptions are said to be complete. Can we design complete algorithms with soft zero tests? We address the basic problem of determining the geometry of the roots of a complex analytic function f. We assume effective box functions for f and its higher derivatives are provided. The problem is formalized as the root clustering problem, and we provide a complete (δ,∈)-exact algorithm based on soft zero tests.

Original languageEnglish (US)
Title of host publicationThe Nature of Computation
Subtitle of host publicationLogic, Algorithms, Applications - 9th Conference on Computability in Europe, CiE 2013, Proceedings
Pages434-444
Number of pages11
DOIs
StatePublished - Jul 26 2013
Event9th Conference on Computability in Europe - The Nature of Computation: Logic, Algorithms, Applications, CiE 2013 - Milan, Italy
Duration: Jul 1 2013Jul 5 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7921 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th Conference on Computability in Europe - The Nature of Computation: Logic, Algorithms, Applications, CiE 2013
CountryItaly
CityMilan
Period7/1/137/5/13

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yap, C., Sagraloff, M., & Sharma, V. (2013). Analytic root clustering: A complete algorithm using soft zero tests. In The Nature of Computation: Logic, Algorithms, Applications - 9th Conference on Computability in Europe, CiE 2013, Proceedings (pp. 434-444). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7921 LNCS). https://doi.org/10.1007/978-3-642-39053-1_51