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TitleNumerical conditioning of a system of algebraic equations with a finite number of solutions using Gröbner bases
Author(s) Antonio Montes
TypeArticle in Journal
AbstractIt is known that Groebner bases approach can be useful to solve systems of algebraic equations with a finite number of solutions. Nevertheless, as stated in [Bu], numerical accuracy attainable when using floating point arithmetic is not yet studied. In this paper we discuss numerical approach, defining conveniently the condition number of every root, and the numerical g.c.d.'s of Buchberger's algorithm. With these instruments we are able to compute confidence-intervals for the roots. We complete the study with two illustrative examples. We also give some insight about the best order of the variables when pure lexicographical order is concerned.
ISSN0163-5824
URL doi.acm.org/10.1145/152379.152387
LanguageEnglish
JournalSIGSAM Bulletin
Volume27
Number1
Pages12-19
PublisherACM Press
AddressNew York, NY, USA
Year1993
MonthJanuary
Translation No
Refereed No
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