Dyadic Hermite interpolation on a rectangular mesh

: Given f and rf 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 de ned on a dense subset of R. Su cient conditions are found in order to extend f to a C1 function. Moreover in nite products and generalized radii of matrices are used to study the convergence to a C1 function. This convergence depends on the ve parameters introduced in the algorithm. AMS subject classi cation: 41A05, 63D05

• Type: Journal
• Year: 1999
• Where: ADCM
• Authors: Serge Dubuc, Jean-Louis Merrien
• Keywords: ADCM 1999, C1 Function, Disjoint Rectangle, Rectangle