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Lattice Rules : Numerical Integration, Approximation, and Discrepancy /

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,...

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Bibliographic Details
Main Authors: Dick, Josef (Author), Kritzer, Peter (Author), Pillichshammer, Friedrich (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2022.
Edition:1st ed. 2022.
Series:Springer Series in Computational Mathematics, 58
Subjects:
Numerical analysis.
Computer science-Mathematics.
Numerical Analysis.
Mathematics of Computing.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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.