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Zbl 0635.65006
Kobza, Jiří
An algorithm for biparabolic spline. (English)
[J] Apl. Mat. 32, 401-413 (1987). ISSN 0373-6725

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. \par 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.
[V.V.Kobkov]

MSC 2000:: *65D07 Splines (numerical methods)
65D05 Interpolation (numerical methods)
41A15 Spline approximation
41A63 Multidimensional approximation problems

Keywords: surface approximations; two-dimensional parabolic interpolation spline; interpolation biparabolic spline; local parameters; parabolic spline algorithms

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