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Titlebook: Lattice Rules; Numerical Integratio Josef Dick,Peter Kritzer,Friedrich Pillichshammer Book 2022 The Editor(s) (if applicable) and The Autho

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书目名称Lattice Rules
副标题Numerical Integratio
编辑Josef Dick,Peter Kritzer,Friedrich Pillichshammer
视频video
概述Accessible introduction for undergraduate students in mathematics or computer science.Discusses practical applications.Explanations of the basic concepts and current methods used in research
丛书名称Springer Series in Computational Mathematics
图书封面Titlebook: Lattice Rules; Numerical Integratio Josef Dick,Peter Kritzer,Friedrich Pillichshammer Book 2022 The Editor(s) (if applicable) and The Autho
描述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..
出版日期Book 2022
关键词lattice rules; numerical integration; quasi Monte Carlo methods; function approximation; worst-case erro
版次1
doihttps://doi.org/10.1007/978-3-031-09951-9
isbn_softcover978-3-031-09953-3
isbn_ebook978-3-031-09951-9Series ISSN 0179-3632 Series E-ISSN 2198-3712
issn_series 0179-3632
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Lattice Rules978-3-031-09951-9Series ISSN 0179-3632 Series E-ISSN 2198-3712
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Extensible Lattice Point Sets,However, the situation is different if we ask for an extension with respect to the number of points, .. Extending the number of points may be of practical relevance if one wants to improve the accuracy of approximation of an integral by increasing the number of integration nodes without having to discard previously computed function values.
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Integration with Respect to Probability Measures,In general, one can apply a transformation to obtain an integral over the unit cube. However, this changes the integrand, and often certain smoothness assumptions are not satisfied anymore by the transformed integrand. Using this approach one can obtain bounds on the integration error for a number of important choices of probability densities.
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