Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form

DOI10.1016/j.apnum.2011.07.009zbMath1227.65020OpenAlexW2005679388MaRDI QIDQ643356

Roberto Barrio, Li-Zhi Cheng, Hao Jiang, Xiang-Ke Liao

Publication date: 28 October 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.07.009

zbMATH Keywords

numerical experimentsround-off errorcomputer aided geometric designBernsteinde Casteljau algorithmbivariate polynomialcompensated algorithmerror-free transformationBézier form

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Uses Software

• mctoolbox
• LBNL
• XBLAS

Cites Work

• Unnamed Item
• Accurate evaluation of a polynomial and its derivative in Bernstein form
• Running error analysis of evaluation algorithms for bivariate polynomials in barycentric Bernstein form
• Algorithms for accurate, validated and fast polynomial evaluation
• Evaluation algorithms for multivariate polynomials in Bernstein-Bézier form
• Efficient evaluation of multivariate polynomials
• A floating-point technique for extending the available precision
• Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest
• A Fortran 90-based multiprecision system
• Evaluation and approximate evaluation of the multivariate Bernstein-Bézier form on a regularly partitioned simplex
• A unified approach to evaluation algorithms for multivariate polynomials
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Accurate Sum and Dot Product

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