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Nearly optimal interpolation of data in \(C^2 (\mathbb{R}^2)\). I. (English) Zbl 1275.65007

Summary: Given \(\epsilon > 0\), we compute a function taking prescribed values at \(N\) given points in \(\mathbb{R}^2\), whose \(C^2\)-norm is within a factor \((1 + \epsilon)\) of least possible. The computation takes \(C(\epsilon)N\log N\) computer operations.

MSC:

65D05 Numerical interpolation
41A05 Interpolation in approximation theory