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Approximation by Smooth Bivariate Splines on a Three-Direction Mesh.

Author: Rong-qing Jia; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center MAR 1983.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Univariate splines have been proved quite useful in practice. However, if one wants to fit a surface, or solve a partial differential equation numerically, one would naturally think of using multivariate splines. Here splines still mean piecewise polynomial functions. In this respect, a basic question is to ascertain, for a given mesh delta and a family S of splines on delta, what its optimal approximation order is.  Read more...
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Document Type: Book
All Authors / Contributors: Rong-qing Jia; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227581482
Description: 27 p.

Abstract:

Univariate splines have been proved quite useful in practice. However, if one wants to fit a surface, or solve a partial differential equation numerically, one would naturally think of using multivariate splines. Here splines still mean piecewise polynomial functions. In this respect, a basic question is to ascertain, for a given mesh delta and a family S of splines on delta, what its optimal approximation order is. This question is challenging even for a regular triangular mesh delta, as soon as one demands that the approximating functions have a certain amount of smoothness. The report records a step toward answering the above question. (Author).

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