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Interpolating and smoothing biquadratic spline. (English) Zbl 0835.41016

Summary: The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and their bases are given by the so-called fundamental splines.

MSC:

41A15 Spline approximation
41A05 Interpolation in approximation theory
65D05 Numerical interpolation
65D07 Numerical computation using splines
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References:

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