Sur les formules de quadrature numérique à nombre minimal de noeuds d’intégration. (French) Zbl 0579.65022

We search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulas on sets of \({\mathbb{R}}^ n\) with weight function which have a minimal number of knots and which are exact on the space \(Q_ k\) of all polynomials of degree \(\leq k\) respectively to each variable \(x_ i\), \(1\leq i\leq n\). These results, completed by original numerical examples in \({\mathbb{R}}^ 2\), adapt to the spaces \(Q_ k\) these proved by H. J. Schmid [ibid. 31, 281-297 (1978; Zbl 0427.65014)] in the case of polynomial spaces \(P_ k\).


65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems


Zbl 0427.65014
Full Text: DOI EuDML


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