Running error analysis of evaluation algorithms for bivariate polynomials in barycentric Bernstein form

DOI10.1007/s00607-005-0149-8zbMath1087.65019OpenAlexW1980316691MaRDI QIDQ818856

Juan Manuel Peña, Esmeralda Mainar

Publication date: 21 March 2006

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-005-0149-8

zbMATH Keywords

stabilitynumerical experimentsde Casteljau algorithmforward errorrunning errorRoundoff errorbivariate polynomials defined on a triangleVS algorithm

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Computer-aided design (modeling of curves and surfaces) (65D17) Real polynomials: analytic properties, etc. (26C05)

Related Items

Evaluation algorithms for multivariate polynomials in Bernstein-Bézier form, On the accuracy of de Casteljau-type algorithms and Bernstein representations, On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis, Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form, Compensated de Casteljau algorithm in \(K\) times the working precision

Uses Software

• mctoolbox

Cites Work

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• Efficient evaluation of multivariate polynomials
• Optimally stable multivariate bases
• On the \(p\)-norm condition number of the multivariate triangular Bernstein basis
• Error analysis of corner cutting algorithms
• The evaluation of the zeros of ill-conditioned polynomials. I, II
• Accuracy and Stability of Numerical Algorithms
• On the multivariate Horner scheme. II: Running error analysis