On multivariate Hermite interpolation

Springer Science and Business Media LLC - Tập 4 - Trang 207-259 - 1995
Thomas Sauer1, Yuan Xu2
1Mathematical Institute, University Erlangen-Nuremberg, Erlangen, Germany
2Department of Mathematics, University of Oregon, Eugene, USA

Tóm tắt

We study the problem of Hermite interpolation by polynomials in several variables. A very general definition of Hermite interpolation is adopted which consists of interpolation of consecutive chains of directional derivatives. We discuss the structure and some aspects of poisedness of the Hermite interpolation problem; using the notion of blockwise structure which we introduced in [10], we establish an interpolation formula analogous to that of Newton in one variable and use it to derive an integral remainder formula for a regular Hermite interpolation problem. For Hermite interpolation of degreen of a functionf, the remainder formula is a sum of integrals of certain (n + 1)st directional derivatives off multiplied by simplex spline functions.

Tài liệu tham khảo

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Springer Science and Business Media LLC

Tập 4

207-259

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