论文信息 - Splines via dynamic programming

Splines via dynamic programming

Abstract Approximating a function with prescribed values at given points on a real interval by a cubic spline is based on the minimum curvature property of the approximation. This essential feature can be used as the criterion to determine the cubic polynomial approximation in each interval in a sequential manner by methods of dynamic programming. A stable system of recurrence relations for the coefficients of the spline in successive intervals is obtained by the methods of dynamic programming and they are shown to be identical with the usual relations of the spline approximation. Extension of this method to other types of splines is also considered.

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