On the numerical condition of BernsteinBézier subdivision processes
Authors:
R. T. Farouki and C. A. Neff
Journal:
Math. Comp. 55 (1990), 637647
MSC:
Primary 65D10; Secondary 65D15, 68T10, 68U05
MathSciNet review:
1035933
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Abstract: The linear map M that takes the Bernstein coefficients of a polynomial on a given interval [a, b] into those on any subinterval is specified by a stochastic matrix which depends only on the degree n of and the size and location of relative to [a, b]. We show that in the norm, the condition number of M has the simple form , where and are the barycentric coordinates of the subinterval midpoint , and f denotes the "zoom" factor of the subdivision map. This suggests a practical ruleofthumb in assessing how far Bézier curves and surfaces may be subdivided without exceeding prescribed (worstcase) bounds on the typical errors in their control points. The exponential growth of with n also argues forcefully against the use of highdegree forms in computeraided geometric design applications.
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 , The algebraic eigenvalue problem, Oxford Univ. Press, 1988. MR 950175 (89j:65031)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199010359330
PII:
S 00255718(1990)10359330
Article copyright:
© Copyright 1990 American Mathematical Society
