Abstract
Given f and ∇f at the vertices of a rectangular mesh, we build an interpolating function f by a subdivision algorithm. The construction on each elementary rectangle is independent of any disjoint rectangle. From the Hermite data associated with the vertices of a rectangle R, the function f is defined on a dense subset of R. Sufficient conditions are found in order to extend f to a C 1 function. Moreover, infinite products and generalized radii of matrices are used to study the convergence to a C 1 function. This convergence depends on the five parameters introduced in the algorithm.
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Dubuc, S., Merrien, JL. Dyadic Hermite interpolation on a rectangular mesh. Advances in Computational Mathematics 10, 343–365 (1999). https://doi.org/10.1023/A:1018943002601
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DOI: https://doi.org/10.1023/A:1018943002601