Lattice rules : numerical integration, approximation, and discrepancy

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

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, J. (Josef) (Author), Kritzer, Peter (Mathematician) (Author), Pillichshammer, Friedrich (Author)
Format: eBook
Language:English
Published: Cham : Springer, [2022]
Series:Springer series in computational mathematics ; 58.
Subjects:
Lattice theory.
Retículos, Teoría de
Lattice theory
Online Access:Click for online access
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.

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