Abstract
This paper addresses a new approach in solving the problem of shape preserving spline interpolation. Based on the formulation of the latter problem as a differential multipoint boundary value problem for hyperbolic and biharmonic tension splines we consider its finite-difference approximation. The resulting system of linear equations can be efficiently solved either by direct (Gaussian elimination) and iterative methods (successive over-relaxation (SOR) method and finite-difference schemes in fractional steps). We consider the basic computational aspects and illustrate the main advantages of this original approach.
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Kvasov, B.I. (2005). DMBVP for Tension Splines. In: Drmač, Z., Marušić, M., Tutek, Z. (eds) Proceedings of the Conference on Applied Mathematics and Scientific Computing. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3197-1_3
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DOI: https://doi.org/10.1007/1-4020-3197-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3196-0
Online ISBN: 978-1-4020-3197-7
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