Recursive de Casteljau bisection and rounding errors

Authors:
Przemysław Kiciak;Ahmed Zidna
Affiliations:
Instytut Matematyki Stosowanej i Mechaniki, Uniwersytet Warszawski ul, Banacha 2, 02-097 Warszawa, Poland;Laboratoire d'Informatique Théorique et Appliquée, Ile du Saulcy 57045 Metz, France
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

Rounding errors of the de Casteljau bisection algorithm applied recursively to finding zeros of polynomials of one or more variables are analyzed. Apart from error bounds for this procedure, the paper contains a proof of the so called numerical variation diminishing property (formulated for one-dimensional case), which is significant in practical procedures of solving algebraic equations.