| Description |
1 online resource (xvi, 580 pages) : color illustrations |
| Series |
Springer series in computational mathematics, 2198-3712 ; volume 58 |
|
Springer series in computational mathematics ; 58. 2198-3712
|
| 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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed July 26, 2022) |
| Subject |
Lattice theory.
|
|
Retículos, Teoría de
|
|
Lattice theory
|
| Form |
Electronic book
|
| Author |
Kritzer, Peter (Mathematician), author.
|
|
Pillichshammer, Friedrich, author.
|
| ISBN |
9783031099519 |
|
3031099516 |
|
9788303109958 |
|
8303109952 |
|
