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Convergence of Bivariate Cardinal Interpolation.

Author: C D Boor; K Hoellig; S Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center MAY 1984.
Edition/Format:   Print book : English
Database:WorldCat
Summary:
This is a follow-up on a previous report in which the authors introduced and studied interpolation by a linear combination of translates of a bivariate box spline on a three-direction mesh. This is of interest because these box splines are not just tensor products of univariate B-splines but are genuinely bivariate, yet are true generalizations of the univariate cardinal B-spline. This allows one to be guided by  Read more...
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Document Type: Book
All Authors / Contributors: C D Boor; K Hoellig; S Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227618148
Notes: See also Rept. no. MRC-TSR-2485, AD-A127 939.
Description: 21 pages

Abstract:

This is a follow-up on a previous report in which the authors introduced and studied interpolation by a linear combination of translates of a bivariate box spline on a three-direction mesh. This is of interest because these box splines are not just tensor products of univariate B-splines but are genuinely bivariate, yet are true generalizations of the univariate cardinal B-spline. This allows one to be guided by Schoenberg's highly successful analysis of univariate cardinal splines, while at the same time struggling with a more complicated setup. The specific task of the present report is the derivation of necessary and of sufficient conditions for the convergence of the box spline interpolants as the degree goes to infinity. The conditions are stated in terms of the Fourier transform of the interpolant.

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