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Distance Matrices and Ridge Function Interpolation

Published online by Cambridge University Press:  20 November 2018

Les Reid
Affiliation:
Department of Mathematics Southwest Missouri State University Springfield, Missouri 65804 USA.
Xingping Sun
Affiliation:
Department of Mathematics Southwest Missouri State University Springfield, Missouri 65804 USA.
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Abstract

A geometric characterization is given for a collection of points in ℝd to produce a singular l1 -distance matrix. Some quantitative results are established in terms of "characteristic matrices". The results in this paper generalize those of Dyn, Light and Cheney and have application to ridge function interpolation.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

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[L] Light, W.A., The singularity of distance matrices. In: Multivariate Approximation Theory, (eds. Schempp, W., Chui, C. and Zeller, K.), Birkhauser-Verlag (1989), 233240.Google Scholar
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[SX] Sun, X., Multivariate interpolation by a general class of functions , J. Approx. Theory, to appear.Google Scholar
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