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A Simple Approach to the Variational Theory for Interpolation on Spheres

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New Developments in Approximation Theory

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 132))


In this paper we consider the problem of developing a variational theory for interpolation by radial basis functions on spheres. The interpolants have the property that they minimise the value of a certain semi-norm, which we construct explicitly. We then go on to investigate forms of the interpolant which are suitable for computation. Our main aim is to derive error bounds for interpolation from scattered data sets, which we do in the final section of the paper.

Research partially supported by NATO grant CRG910885

Research partially supported by EPSRC grant GR/K79710

Research partially supported by EPSRC grant GR/J19481

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© 1999 Springer Basel AG

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Levesley, J., Light, W., Ragozin, D., Sun, X. (1999). A Simple Approach to the Variational Theory for Interpolation on Spheres. In: Müller, M.W., Buhmann, M.D., Mache, D.H., Felten, M. (eds) New Developments in Approximation Theory. ISNM International Series of Numerical Mathematics, vol 132. Birkhäuser, Basel.

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  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9733-4

  • Online ISBN: 978-3-0348-8696-3

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