國立虎尾科技大學 |

Lattice Rules = Numerical Integration, Approximation, and Discrepancy /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lattice Rules/ by Josef Dick, Peter Kritzer, Friedrich Pillichshammer.
Reminder of title:	Numerical Integration, Approximation, and Discrepancy /
Author:	Dick, Josef.
other author:	Kritzer, Peter.
Description:	XVI, 580 p. 32 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Numerical analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-09951-9
ISBN:	9783031099519

Lattice Rules = Numerical Integration, Approximation, and Discrepancy /
Dick, Josef.

Lattice RulesNumerical Integration, Approximation, and Discrepancy /[electronic resource] :by Josef Dick, Peter Kritzer, Friedrich Pillichshammer. - 1st ed. 2022. - XVI, 580 p. 32 illus. in color.online resource. - Springer Series in Computational Mathematics,582198-3712 ;. - Springer Series in Computational Mathematics,48.

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:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Lattice Rules = Numerical Integration, Approximation, and Discrepancy /
LDR:02739nam a22004095i 4500 001 1088902
003 DE-He213
005 20220723153812.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031099519 $9 978-3-031-09951-9
024 7 $a 10.1007/978-3-031-09951-9 $2 doi
035 $a 978-3-031-09951-9
050 4 $a QA297-299.4
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518 $2 23
100 1 $a Dick, Josef. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1079566
245 1 0 $a Lattice Rules $h [electronic resource] : $b Numerical Integration, Approximation, and Discrepancy / $c by Josef Dick, Peter Kritzer, Friedrich Pillichshammer.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XVI, 580 p. 32 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Series in Computational Mathematics, $x 2198-3712 ; $v 58
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.
650 0 $a Numerical analysis. $3 527939
650 0 $a Computer science—Mathematics. $3 1253519
650 1 4 $a Numerical Analysis. $3 671433
650 2 4 $a Mathematics of Computing. $3 669457
700 1 $a Kritzer, Peter. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396126
700 1 $a Pillichshammer, Friedrich. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396127
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031099502
776 0 8 $i Printed edition: $z 9783031099526
776 0 8 $i Printed edition: $z 9783031099533
830 0 $a Springer Series in Computational Mathematics, $x 0179-3632 ; $v 48 $3 1258881
856 4 0 $u https://doi.org/10.1007/978-3-031-09951-9
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)