OPTIMAL CONDITIONING OF BERNSTEIN COLLOCATION MATRICES

被引：12

作者：

Delgado, Jorge ^{[1
]}

Pena, J. M. ^{[2
]}

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, Escuela Univ Politecn Teruel, E-44071 Teruel, Spain

[2] Univ Zaragoza, Dept Matemat Aplicada, E-50009 Zaragoza, Spain

来源：

关键词：

totally positive matrices; conditioning; Bernstein polynomials; STABILITY; ALGORITHM;

D O I：

10.1137/080737976

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some results on the optimal conditioning of the collocation matrices of the Bernstein basis are provided. Numerical examples illustrate the results.

引用

页码：990 / 996

页数：7

共 13 条

[1] TOTALLY POSITIVE MATRICES
ANDO, T
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 90 : 165 - 219
[2] [Anonymous], 1996, TOTAL POSITIVITY ITS
[3] Bauer F. L., 1963, Numer. Math., V5, P73
[4] Carnicer J. M., 1993, ADV COMPUT MATH, V1, P173, DOI [10.1007/BF02071384, DOI 10.1007/BF02071384]
[5] A shape preserving representation with an evaluation algorithm of linear complexity.
Delgado, J
Peña, JM
[J]. COMPUTER AIDED GEOMETRIC DESIGN, 2003, 20 (01) : 1 - 10
[6] Farouki R. T., 1987, Computer-Aided Geometric Design, V4, P191, DOI 10.1016/0167-8396(87)90012-4
[7] On the stability of polynomial transformations between Taylor, Bernstein and Hermite forms
Hermann, T
[J]. NUMERICAL ALGORITHMS, 1996, 13 (3-4) : 307 - 320
[8] Higham N. J., 2002, Accuracy and stability of numerical algorithms
[9] Karlin S., 1968, Total positivity, VVolume 1
[10] MARCO A, 2008, POLYNOMIAL LEAST SQU