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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
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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:
  • MathSciNet review: 1122061