Lattice Rules
Numerical Integration, Approximation, and Discrepancy
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ISBN-13:
9783031099533
Veröffentl:
2023
Einband:
Paperback
Erscheinungsdatum:
24.07.2023
Seiten:
596
Autor:
Josef Dick
Gewicht:
890 g
Format:
235x155x32 mm
Serie:
58, Springer Series in Computational Mathematics
Sprache:
Englisch
Beschreibung:
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.
Accessible introduction for undergraduate students in mathematics or computer science
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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