Semi-cardinal interpolation and difference equations: from cubic B-splines to a three-direction box-spline construction

Authors:
Aurelian Bejancu
Affiliations:
Department of Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds, UK and Department of Mathematics and Computer Science, Kuwait University, Safat, Kuwait
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 2

Box splines

Box splines
Elementary Numerical Analysis: An Algorithmic Approach

Elementary Numerical Analysis: An Algorithmic Approach

Semi-cardinal polyspline interpolation with Beppo Levi boundary conditions

Journal of Approximation Theory
Symmetric box-splines on the A*n lattice

Journal of Approximation Theory

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Abstract

This paper considers the problem of interpolation on a semi-plane grid from a space of box-splines on the three-direction mesh. Building on a new treatment of univariate semi-cardinal interpolation for natural cubic splines, the solution is obtained as a Lagrange series with suitable localization and polynomial reproduction properties. It is proved that the extension of the natural boundary conditions to box-spline semi-cardinal interpolation attains half of the approximation order of the cardinal case.