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MSC: 41A05, 41A15, 65D05
smooth interpolation; data interpolation; cubic spline interpolation; Fourier series
A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $\exp(-\ii kx)$. A 1D numerical example is presented.
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