Computational Aspects of Polynomial Interpolation in Several Variables
نویسنده
چکیده
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 ne , which is related to Gauss elimination applied to the Vandermonde matrix (öa)öee a£Zd for 8. We also discuss some attractive properties of the above assignment and algorithmic details, and present some bivariate examples. We say that the pair (6, P) of a (finite) point set OcK1' and a (polynomial) space P of functions on Rd is correct if the restriction map
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