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Lattice rules : numerical integration, approximation, and discrepancy / Josef Dick, Peter Kritzer, Friedrich Pillichshammer.

Dick, J. (Josef), author.; Kritzer, Peter (Mathematician), author.; Pillichshammer, Friedrich, author.
2022
QA171.5
Available Online
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Title
Lattice rules : numerical integration, approximation, and discrepancy / Josef Dick, Peter Kritzer, Friedrich Pillichshammer.
Author
Dick, J. (Josef), author.
ISBN
9783031099519 (electronic bk.)
3031099516 (electronic bk.)
9783031099502
3031099508
DOI
https://doi.org/10.1007/978-3-031-09951-9
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xvi, 580 pages) : color illustrations.
Item Number
10.1007/978-3-031-09951-9 doi
Call Number
QA171.5
Dewey Decimal Classification
511.3/3
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 26, 2022).
Added Author
Kritzer, Peter (Mathematician), author.
Pillichshammer, Friedrich, author.
Series
Springer series in computational mathematics ; 58.
Available in Other Form
Print version: 9783031099502
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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.

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