Dyadic Hermite interpolation on a rectangular mesh
- Cite this article as:
- Dubuc, S. & Merrien, JL. Advances in Computational Mathematics (1999) 10: 343. doi:10.1023/A:1018943002601
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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 C1 function. Moreover, infinite products and generalized radii of matrices are used to study the convergence to a C1 function. This convergence depends on the five parameters introduced in the algorithm.