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Beatson, R.K.* ; zu Castell, W.

Thinplate splines on the sphere.

Symmetry Integr. Geom. Methods Appl. 14:083 (2018)
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In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for Rdwere introduced by Duchon and have become a widely used tool in myriad applications. The analogues for Sd−1are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the S2case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Gegenbauer Polynomials ; Positive Definite Functions ; Thinplate Splines ; Ultraspherical Expansions ; Zonal Functions; Positive-definite Functions; Interpolation
e-ISSN 1815-0659
Quellenangaben Volume: 14, Issue: , Pages: , Article Number: 083 Supplement: ,
Publisher SIGMA
Publishing Place 3 Tereschchenkiv Ska St, Kyiv 4, 01601, Ukraine
Reviewing status