Computational aspects of polynomial interpolation in several variables
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- by Carl de Boor and Amos Ron PDF
- Math. Comp. 58 (1992), 705-727 Request permission
Abstract:
The pair $\langle \Theta ,P\rangle$ of a point set $\Theta \subset {\mathbb {R}^d}$ and a polynomial space P on ${\mathbb {R}^d}$ is correct if the restriction map $P \to {\mathbb {R}^\Theta }:p \mapsto {p_{|\Theta }}$ is invertible, i.e., if there is, for any f defined on $\Theta$, a unique $p \in P$ which matches f on $\Theta$. We discuss here a particular assignment $\Theta \mapsto {\Pi _\Theta }$, introduced by us previously, for which $\langle \Theta ,{\Pi _\Theta }\rangle$ is always correct, and provide an algorithm for the construction of a basis for ${\Pi _\Theta }$, which is related to Gauss elimination applied to the Vandermonde matrix ${({\vartheta ^\alpha })_{\vartheta \in \Theta ,\alpha \in \mathbb {Z}_ + ^d}}$ for $\Theta$. We also discuss some attractive properties of the above assignment and algorithmic details, and present some bivariate examples.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp. 58 (1992), 705-727
- MSC: Primary 65D05; Secondary 41A05, 41A63
- DOI: https://doi.org/10.1090/S0025-5718-1992-1122061-0
- MathSciNet review: 1122061