Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form

• Published in: Computing Vol. 77; no. 1; pp. 97 - 111
• Main Authors: Mainar, E., Peña, J. M.
• Format: Journal Article
• Language: English
• Published: Wien Springer 01.02.2006; Springer Nature B.V
• Subjects: Algorithms; Approximations and expansions; Error analysis; Exact sciences and technology; Experiments; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Polynomials; Sciences and techniques of general use; Studies; Error estimation; Rounding error; 41A15. Roundoff error; Bernstein polynomial; Numerical analysis; forward error; Algorithm complexity; Running error; 41A10; 65D17; De Casteljau algorithm; bivariate polynomials defined on a triangle; Algorithm analysis; Numerical stability; VS algorithm; 65G05
• ISSN: 0010-485X; 1436-5057
• DOI: 10.1007/s00607-005-0149-8

Running error analysis for the bivariate de Casteljau algorithm and the VS algorithm is performed. Theoretical results joint with numerical experiments show the better stability properties of the de Casteljau algorithm for the evaluation of bivariate polynomials defined on a triangle in spite of the lower complexity of the VS algorithm. The sharpness of our running error bounds is shown. [PUBLICATION ABSTRACT]