Bivariate spline interpolation at grid points |
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Authors: | G Nürnberger Th Riessinger |
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Institution: | Universit?t Mannheim,
Fakult?t für Mathematik und Informatik,
D-68131 Mannheim, Germany, DE Fachhochschule Frankfurt a. M.,
Fachbereich MND,
D-60318 Frankfurt a. M., Germany, DE
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Abstract: | Summary.
We describe algorithms for constructing point sets at which interpolation by
spaces of bivariate splines of arbitrary degree and smoothness is
possible. The splines are defined on rectangular partitions adding
one or two diagonals to each rectangle. The interpolation sets
are selected in such a way that the grid points of the partition
are contained in these sets, and no large linear systems have to be solved.
Our method is to generate a net of line segments and to choose point sets in
these segments which satisfy the Schoenberg-Whitney condition for
certain univariate spline spaces such that a principle of degree
reduction can be applied. In order to include the grid points in the
interpolation sets, we give a sufficient Schoenberg-Whitney type
condition for interpolation by bivariate splines supported in certain cones.
This approach is completely different
from the known interpolation methods for bivariate splines of degree at most
three. Our method is illustrated by some numerical examples.
Received
October 5, 1992 / Revised version received May 13, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 41A15 41A63 65D05 65D07 |
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