Open Access Open Access  Restricted Access Subscription or Fee Access

On Lagrange and Hermite Interpolation Along Algebraic Manifold

Xue-Zhang Liang, Ming Zhang


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.