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Best bounds on the approximation of polynomials and splines by their control structure

✍ Scribed by Ulrich Reif

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
113 KB
Volume
17
Category
Article
ISSN
0167-8396

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✦ Synopsis

We present best bounds on the deviation between univariate polynomials, tensor product polynomials, BΓ©zier triangles, univariate splines, and tensor product splines and the corresponding control polygons and nets. Both pointwise estimates and bounds on the L p -norm are given in terms of the maximum of second differences of the control points. The given estimates are sharp for control points corresponding to arbitrary quadratic polynomials in the univariate case, and to special quadratic polynomials in the bivariate case.

πŸ“œ SIMILAR VOLUMES

Approximation of Functions on [βˆ’1,1] and
Approximation of Functions on [βˆ’1,1] and Their Derivatives by Polynomial Projection Operators
✍ K. BalΓ‘zs; T. Kilgore πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 241 KB

## Abstract Pointwise estimates are obtained for the simultaneous approximation of a function f Ο΅__C__^__q__^[‐1,1] and its derivatives f^(1)^, …, f^(q)^ by means of an arbitrary sequence of bounded linear projection operators __L__~__n__~ which map __C__[‐1,1] into the polynomials of degree at mos