Abstract
This paper is concerned with range restricted interpolation of gridded data by biquadratic and biquartic tensor product splines on refined rectangular grids. In particular, the given lower and upper bounds are assumed to be continuous and piecewise bilinear with respect to the original grid. Sufficient conditions for the fulfillment of the range restrictions are derived utilizing the tensor product structure as well as corresponding results for univariate quadratic and quartic splines with additional knots. The solvability of this system of sufficient conditions, hence the existence of interpolants meeting the constraints, can always be achieved for strictly compatible data by constructing the refined grid appropriately. The selection of a visually improved range restricted interpolant is based on a fit-and-modify approach or on the minimization of a bivariate Holladay functional.
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© 1996 B. G. Teubner Stuttgart
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Mulansky, B., Schmidt, J.W., Walther, M. (1996). Tensor Product Spline Interpolation subject to Piecewise Bilinear Lower and Upper Bounds. In: Hoschek, J., Kaklis, P.D. (eds) Advanced Course on FAIRSHAPE. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-82969-6_16
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DOI: https://doi.org/10.1007/978-3-322-82969-6_16
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-519-02634-1
Online ISBN: 978-3-322-82969-6
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