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Bivariate Cardinal Interpolation by Splines on a Three-Direction Mesh.

Author: Carl de Boor; Klaus Hoellig; Sherman Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center MAR 1983.
Edition/Format:   Book : English
Database:WorldCat
Summary:
In a series of monographs Schogenberg developed a comprehensive theory of univariate cardinal splines. His results strongly influenced the analysis of totally positive matrices. In this report the author extend two of his basic results on cardinal interpolation to bivariate box-splines. They show that, for functions of exponential type, cardinal interpolation is a rapidly convergent approximation process as the  Read more...
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Document Type: Book
All Authors / Contributors: Carl de Boor; Klaus Hoellig; Sherman Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227581147
Description: 40 p.

Abstract:

In a series of monographs Schogenberg developed a comprehensive theory of univariate cardinal splines. His results strongly influenced the analysis of totally positive matrices. In this report the author extend two of his basic results on cardinal interpolation to bivariate box-splines. They show that, for functions of exponential type, cardinal interpolation is a rapidly convergent approximation process as the degree tends to infinity. Being not restricted to a tensor product mesh gives a greater flexibility, and because of the exponential decay of the Lagrange functions, spline interpolation is suitable, e.g., for data smoothing. They also expect that bivariate cardinal splines have a similar significance for theoretical questions as in the univariate case.

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