Efficient cubature rules
نویسندگان
چکیده
منابع مشابه
Cubature Rules of Prescribed Merit
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for the hypercube: this is the merit of a rule which is closely related to its trigonometric degree and which reduces to the Zaremba figure of merit in the case of a lattice rule. We derive a family of rules Q k having dimension s and merit 2. These rules seem to be competitive with lattice rules with...
متن کاملSymbolic–numeric Gaussian cubature rules
Article history: Received 22 June 2010 Received in revised form 11 March 2011 Accepted 14 March 2011 Available online 2 April 2011
متن کاملMinimal cubature rules on an unbounded domain
A family of minimal cubature rules is established on an unbounded domain, which is the first such family known on unbounded domains. The nodes of such cubature rules are common zeros of certain orthogonal polynomials on the unbounded domain, which are also constructed. 2000 AMS subject classification: 41A05, 65D05, 65D32.
متن کاملMarkov cubature rules for polynomial processes
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractab...
متن کاملThe Construction of cubature rules for multivariate highly oscillatory integrals
We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of the integrand and its derivatives in a limited set of points. A general method is presented to identify these points and to compute the weights of the corresponding rule. The accuracy of the constructed...
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ژورنال
عنوان ژورنال: ETNA - Electronic Transactions on Numerical Analysis
سال: 2019
ISSN: 1068-9613,1068-9613
DOI: 10.1553/etna_vol51s219