Lattice Rules, 1st ed. 2022
◆Springer Yellow セール開催中!:2025年6月29日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 Numerical Integration, Approximation, and Discrepancy Series: Springer Series in Computational Mathematics Author: Dick, Josef / Kritzer, Peter / Pillichshammer, Friedrich Publisher: Springer ISBN: 9783031099502 Cover: HARDCOVER Date: 2022年07月 DESCRIPTION * Accessible introduction for undergraduate students in mathematics or computer science * Discusses practical applications * Explanations of the basic concepts and current methods used in research 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. TABLE OF CONTENTS Introduction Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 1-54 Integration of Smooth Periodic Functions Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 55-93 Constructions of Lattice Rules Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 95-139 Modified Construction Schemes Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 141-193 Discrepancy of Lattice Point Sets Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 195-219 Extensible Lattice Point Sets Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 221-264 Lattice Rules for Nonperiodic Integrands Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 265-317 Integration with Respect to Probability Measures Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 319-337 Integration of Analytic Functions Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 339-361 Korobov’s p -Sets Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 363-375 Lattice Rules in the Randomized Setting Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 377-394 Stability of Lattice Rules Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 395-408 L2-Approximation Using Lattice Rules Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 409-456 L ∞ -Approximation Using Lattice Rules Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 457-488 Multiple Rank-1 Lattice Point Sets Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 489-508 Fast QMC Matrix-Vector Multiplication Josef Dick, Peter Kritzer, Friedrich Pillichshammer Pages 509-521
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