ISSN:
1432-0940
Keywords:
Key words. Cubature formula, Polynomial exactness, Universality, Optimal error bounds, Fully symmetric formulas, Sparse grids, Interpolation. AMS Classification. 41A55, 41A63, 65D30, 65D32, 65Y20.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We study cubature formulas for d -dimensional integrals with arbitrary weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree, the number of knots depends on the dimension in an order-optimal way. The cubature formulas are universal: the order of convergence is almost optimal for two different scales of function spaces. The construction is simple: a small number of arithmetical operations is sufficient to compute the knots and the weights of the formulas.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s003659900119
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