Kobza, Jiří An algorithm for biparabolic spline. (English) Zbl 0635.65006 Apl. Mat. 32, 401-413 (1987). 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 Cited in 6 Documents MSC: 65D07 Numerical computation using splines 65D05 Numerical interpolation 41A15 Spline approximation 41A63 Multidimensional problems Keywords:surface approximations; two-dimensional parabolic interpolation spline; interpolation biparabolic spline; local parameters; parabolic spline algorithms × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] C. de Boor: A practical guide to splines. Springer, N. Y. 1978. · Zbl 0406.41003 [2] J. Kobza: On algorithms for parabolic splines. Acta UPO, FRN, Vol. 88, Math. XXVI · Zbl 0693.65005 [3] J. Kobza: Evaluation and mapping of parabolic interpolating spline. (Czech). Knižnica algoritmov, IX. diel, str. 51-58; JSMF Bratislava 1987. [4] В. Л. Макаров В. В. Хлобыстов: Сплайн-аппроксимация функций. Москва, Наука 1983. · Zbl 1229.47001 [5] С. Б. Стечкин И. Н. Субботин: Сплайны в вычислительной математике. Москва, Наука 1976. · Zbl 1226.05083 [6] M. Schultz: Spline analysis. Prentice-Hall, N. J. 1973. · Zbl 0333.41009 [7] Ю. С. Завялое Б. И. Квасов В. Л. Мирошниченко: Методы сплайн-функций. Москва, Наука 1980. · Zbl 1229.60003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.