On Quasi-Monte Carlo Rules Achieving Higher Order Convergence

Josef Dick ()
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Josef Dick: The University of New South Wales, School of Mathematics and Statistics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 73-96 from Springer

Abstract: Abstract Quasi-Monte Carlo rules which can achieve arbitrarily high order of convergence have been introduced recently. The construction is based on digital nets and the analysis of the integration error uses Walsh functions. Various approaches have been used to show arbitrarily high convergence. In this paper we explain the ideas behind higher order quasi-Monte Carlo rules by leaving out most of the technical details and focusing on the main ideas.

Keywords: Quadrature Rule; Generate Matrice; Quadrature Point; Integration Error; Lattice Rule (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_5

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DOI: 10.1007/978-3-642-04107-5_5

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