General interpolation on the lattice h{\Bbb Z}^s: Compactly supported fundamental solutions |
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Authors: | Sherman D Riemenschneider Zuowei Shen |
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Institution: | (1) Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1 , CA;(2) Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511 , SG |
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Abstract: | Summary. In this paper we combine an earlier method developed with K. Jetter on general cardinal interpolation with constructions
of compactly supported solutions for cardinal interpolation to gain compactly supported fundamental solutions for the general
interpolation problem. The general interpolation problem admits the interpolation of the functional and derivative values
under very weak restrictions on the derivatives to be interpolated. In the univariate case, some known general constructions
of compactly supported fundamental solutions for cardinal interpolation are discussed together with algorithms for their construction
that make use of MAPLE. Another construction based on finite decomposition and reconstruction for spline spaces is also provided.
Ideas used in the latter construction are lifted to provide a general construction of compactly supported fundamental solutions
for cardinal interpolation in the multivariate case. Examples are provided, several in the context of some general interpolation
problem to illustrate how easy is the transition from cardinal interpolation to general interpolation.
Received May 11, 1993 / Revised version received August 16, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 42C05 41A63 41A30 41A15 |
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