Accession Number:

ADA142894

Title:

Convergence of Bivariate Cardinal Interpolation.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Report Date:

1984-05-01

Pagination or Media Count:

21.0

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 Schoenbergs 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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE