Lattice rules numerical integration, approximation, and discrepancy / [electronic resource] :

• 作者： Dick, J.
• 其他作者：
  • Kritzer, Peter.
  • Pillichshammer, Friedrich.
  • SpringerLink (Online service)
• 其他題名：
  • Springer series in computational mathematics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Springer series in computational mathematics,v. 58
• 主題： Lattice theory. , Numerical Analysis. , Mathematics of Computing.
• ISBN： 9783031099519 (electronic bk.) 、 9783031099502 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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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• 摘要註: 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.
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