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Bivariate cardinal interpolation by splines on a three-direction mesh. (English) Zbl 0586.41005
This is a delicious paper. The authors are looking for a function which is a bounded cardinal interpolation to bounded data. They carry Schoenberg’s beautiful cardinal spline theory over to a two-dimensional situation. They use Schoenberg’s method, written in ”Contribution, to data smoothing” to describe necessary and sufficient conditions on Fourier transform and to discuss the correctness of the bivariate interpolation problem. They also discuss the convergence of bivariate cardinal interpolation.
Reviewer: Z.X.Xiang

41A15 Spline approximation
41A05 Interpolation in approximation theory
65D07 Numerical computation using splines
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