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Lattice rulesnumerical integration, approximation, and discrepancy /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lattice rulesby Josef Dick, Peter Kritzer, Friedrich Pillichshammer.
其他題名:	numerical integration, approximation, and discrepancy /
作者:	Dick, J.
其他作者:	Kritzer, Peter.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xvi, 580 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Lattice theory.
電子資源:	https://doi.org/10.1007/978-3-031-09951-9
ISBN:	9783031099519

Lattice rulesnumerical integration, approximation, and discrepancy /
Dick, J.

Lattice rulesnumerical integration, approximation, and discrepancy /[electronic resource] :by Josef Dick, Peter Kritzer, Friedrich Pillichshammer. - Cham :Springer International Publishing :2022. - xvi, 580 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v. 582198-3712 ;. - Springer series in computational mathematics ;42..

Introduction -- Integration of Smooth Periodic Functions -- Constructions of Lattice Rules -- Modified Construction Schemes -- Discrepancy of Lattice Point Sets -- Extensible Lattice Point Sets -- Lattice Rules for Nonperiodic Integrands -- Intrgration with Respect to Probability Measures -- Integration of Analytic Functions -- Korobov's p-Sets -- Lattice Rules in the Randomized Setting -- Stability of Lattice Rules -- L2-Approximation Using Lattice Rules -- L∞-Approximation Using Lattice Rules -- Multiple Rank-1 Lattice Point Sets -- Fast QMC Matrix-Vector Multiplication -- Partial Diffeential Equations With Random Coefficients -- Numerical Experiments for Lattice Rule Construction Algorithms -- References -- Index.

Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.

ISBN: 9783031099519

Standard No.: 10.1007/978-3-031-09951-9doiSubjects--Topical Terms:

185633
Lattice theory.

LC Class. No.: QA171.5 / .D53 2022

Dewey Class. No.: 511.33

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505 0 $a Introduction -- Integration of Smooth Periodic Functions -- Constructions of Lattice Rules -- Modified Construction Schemes -- Discrepancy of Lattice Point Sets -- Extensible Lattice Point Sets -- Lattice Rules for Nonperiodic Integrands -- Intrgration with Respect to Probability Measures -- Integration of Analytic Functions -- Korobov's p-Sets -- Lattice Rules in the Randomized Setting -- Stability of Lattice Rules -- L2-Approximation Using Lattice Rules -- L∞-Approximation Using Lattice Rules -- Multiple Rank-1 Lattice Point Sets -- Fast QMC Matrix-Vector Multiplication -- Partial Diffeential Equations With Random Coefficients -- Numerical Experiments for Lattice Rule Construction Algorithms -- References -- Index.
520 $a Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
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