Abstract
We consider the construction of a C (1,1) interpolation parabolic spline function of two variables on a uniform rectangular grid, i.e., a function continuous in a given region together with its first partial derivatives which on every partial grid rectangle is a polynomial of second degree in x and second degree in y. The spline function is constructed as a minimum-derivative one-dimensional quadratic spline in one of the variables, and the spline coefficients themselves are minimum-derivative quadratic spline functions of the other variable.
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Translated from Prikladnaya Matematika i Informatika, No. 33, pp. 101–107, 2009.
An erratum to this article can be found online at http://dx.doi.org/10.1007/s10598-013-9169-y.
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Dmitriev, V.I., Ingtem, Z.G. A two-dimensional minimum-derivative spline. Comput Math Model 21, 206–211 (2010). https://doi.org/10.1007/s10598-010-9065-7
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DOI: https://doi.org/10.1007/s10598-010-9065-7