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Solvability of cardinal spline interpolation problems

Published online by Cambridge University Press:  14 November 2011

T. N. T. Goodman
T. N. T. Goodman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee
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Synopsis

We consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points of a periodic vector x, specified by a periodic incidence matrix G. Similarly, we allow discontinuity of certain derivatives of the piecewise polynomial at certain points of x, specified by a periodic incidence matrix H. This generalises the well-known cardinal spline interpolation of Schoenberg. We investigate conditions on G, H and x under which there is a unique bounded solution for any given bounded data.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 39 - 57
Copyright
Copyright © Royal Society of Edinburgh 1983

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