Abstract
A Newton-type approach is used to deal with bivariate polynomial Hermite interpolation problems when the data are distributed in the intersections of two families of straight lines, as a generalization of regular grids. The interpolation operator is degree-reducing and the interpolation space is a minimal degree space. Integral remainder formulas are given for the Lagrange case, then extended to the Hermite case, and finally used to obtain error estimates.
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