Some researches on trivariate Lagrange interpolation

[摘要] In this paper, in order to go a step further research on the problem of trivariate Lagrange interpolation, we pose the concepts of sufficient intersection of algebraic surfaces and Lagrange interpolation along a space algebraic curve, and extend Cayley-Bacharach theorem in algebraic geometry from R-2 to R-3. By using the conclusion of the extended theorem, we deduce a general method of constructing properly posed set of nodes for Lagrange interpolation along a space algebraic curve, and give a series of corollaries for the practical applications. Moreover, we give a new method of constructing properly posed set of nodes for Lagrange interpolation along an algebraic surface, and as a result we make clear the geometrical structure of it. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2006-10-15

[效力级别]  Proceedings Paper

[关键词] trivariate Lagrange interpolation;Lagrange interpolation along an algebraic surface;Lagrange interpolation along a space algebraic curve;properly posed set of nodes for Lagrange interpolation