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Multivariate interpolation and conditionally positive definite functions. II. (English) Zbl 0859.41004
This paper is a continuation of another of the authors’ paper in Approximation Theory Appl. 4, No. 4, 77-89 (1988; Zbl 0703.41008), which deals with a variational approach to solving scattered data interpolation problems in two or more variables. In particular, in the present paper, the authors use Fourier transforms to give improved descriptions of the basic spaces \(C_h\) in which the interpolation takes place. In addition, they improve the error bounds given in the earlier paper. In certain cases (including the classical multiquadrics), error estimates of arbitrary order are possible.
Reviewer: L.L.Schumaker

MSC:
41A05 Interpolation in approximation theory
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
41A15 Spline approximation
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