Computational aspects of polynomial interpolation in several variables
نویسندگان
چکیده
منابع مشابه
Computational Aspects of Polynomial Interpolation in Several Variables
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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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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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...
متن کاملPolynomial interpolation in several variables
1 0. PREAMBLE I want to thank the organizers for inviting me to this meeting as it gives me the opportunity to help celebrate Sam Conte who gave me my rst academic job. More than that, he provided my children with many years of summer camp in the wilds of New Hampshire and Wisconsin, and at least two of them think that those summers in New Hampshire were essential for their growing up (and I te...
متن کاملUNIVERSITY OF WISCONSIN-MADISON COMPUTER SCIENCES DEPARTMENT Computational aspects of polynomial interpolation in several variables
The pair 〈Θ, P 〉 of a pointset Θ ⊂ IR and a polynomial space P on IR is correct if the restriction map P → IR : p 7→ p|Θ is invertible, i.e., if there is, for any f defined on Θ, a unique p ∈ P which matches f on Θ. We discuss here a particular assignment Θ 7→ ΠΘ, introduced in [3], for which 〈Θ,ΠΘ〉 is always correct, and provide an algorithm for the contruction of a basis for ΠΘ which is relat...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1992
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1992-1122061-0