An algorithm for biparabolic spline. (English) Zbl 0635.65006

Some kinds of algorithms for computing the parameters of a two- dimensional parabolic interpolation spline on a rectangle are studied. With given data and suitable boundary conditions there exists a unique interpolation biparabolic spline which can be constructed in terms of concentrated or dispersed local parameters using corresponding second derivative or first derivative representations.
Two-dimensional computation is split into a sequence of one-dimensional parabolic spline algorithms in which one has to solve systems of linear equations with tridiagonal (or cyclic tridiagonal in the periodic case) matrices. After the values of the parameters are obtained one can calculate the spline via the conventional piecewise-polynomial representation or a special FV-algorithm suggested by the author.
Reviewer: V.V.Kobkov


65D07 Numerical computation using splines
65D05 Numerical interpolation
41A15 Spline approximation
41A63 Multidimensional problems
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