Lattice Rules
Numerical Integration, Approximation, and Discrepancy
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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.
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 Discusses practical applications Explanations of the basic concepts and current methods used in research
Autor*in
Josef Dick
Themen in »Lattice Rules«
lattice rules numerical integration quasi Monte Carlo methods function approximation worst-case error discrepancy information-based complexity tractability