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On Lagrange and Hermite Interpolation Along Algebraic Manifold

Xue-Zhang Liang, Ming Zhang

Abstract


Polynomial interpolation including Lagrange and Hermite interpolation is an important problem in computational mathematics and approximation theory. In this paper, we discuss some special multivariate interpolation problems which lead to the construction of the properly posed set of nodes. In practice, the interpolation along the algebraic manifold often be considered. So we introduce the concept of sufficiently intersected algebraic manifold in n-dimensional space and the interpolation problem along it. And we deduce a general method of constructing properly posed set of nodes for interpolation along an algebraic manifold, namely the superposition interpolation process. As a special case we deeply research polynomial interpolation problem on the unit sphere which include Lagrange and Hermite interpolation problems and get some valuable results.

Keywords


Lagrange interpolation; Hermite interpolation; algebraic manifold; superposition interpolation process

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