Polynomial interpolation in several complex variables
نویسندگان
چکیده
منابع مشابه
Polynomial interpolation in several variables
This is a survey of the main results on multivariate polynomial interpolation in the last twenty five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devo...
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This paper summarizes relations between the constructive theory of polynomial ideals and polynomial interpolation in several variables. The main ingredient is a generalization of the algorithm for division with remainder to \quotients" of polynomials and nite sets of polynomi-als. x1. Introduction When compared to the univariate case, polynomial interpolation in several variables turns out to b...
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When passing from one to several variables, the nature and structure of polynomial interpolation changes completely: the solvability of the interpolation problem with respect to a given finite dimensional polynomial space, like all polynomials of at most a certain total degree, depends not only on the number, but significantly on the geometry of the nodes. Thus the construction of interpolation...
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The pair (6, P) of a point set 8 C R¿ and a polynomial space P on Rd is correct if the restriction map P —» E8 : p t-> P|Q is invertible, i.e., if there is, for any / defined on 0 , a unique p G P which matches /on 9. We discuss here a particular assignment 6 >-+ Fie , introduced by us previously, for which (8, lie) is always correct, and provide an algorithm for the construction of a basis for...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1978
ISSN: 0021-9045
DOI: 10.1016/0021-9045(78)90034-5