Computation of the Bernstein Coefficients on Subdivided Triangles

Computation of the Bernstein Coefficients on Subdivided Triangles We present a procedure for computing the coefficients of the expansion of a bivariate polynomial into Bernstein polynomials over subtriangles. These triangles are generated by partitioning the unit triangle. The coefficients are computed directly from the coefficients on the subdivided triangle from the preceding subdivision level. This allows a recursive computation of the coefficients and facilitates the economical computation of bounds for the range of a bivariate polynomial over a given triangle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Computation of the Bernstein Coefficients on Subdivided Triangles

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009909004274
Publisher site
See Article on Publisher Site

Abstract

We present a procedure for computing the coefficients of the expansion of a bivariate polynomial into Bernstein polynomials over subtriangles. These triangles are generated by partitioning the unit triangle. The coefficients are computed directly from the coefficients on the subdivided triangle from the preceding subdivision level. This allows a recursive computation of the coefficients and facilitates the economical computation of bounds for the range of a bivariate polynomial over a given triangle.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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