Lattice Rules

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.

Josef Dick is a Professor in the School of Mathematics and Statistics at the University of New South Wales in Sydney, Australia. His research focuses on computational mathematics and its applications, in particular, quasi-Monte Carlo methods for integration and approximation, and its applications to Uncertainty Quantification. He works in the area of computational mathematics, in particular quasi-Monte Carlo methods and Uncertainty Quantification. He has been awarded several prices, including the Heyde Medal of the Australian Academy of Science and the Medal of the Australian Mathematical Society. He is a member of the steering committee of the conference series on Monte Carlo and quasi-Monte Carlo methods (MCQMC), a senior Editor of the Journal of Complexity, and an Editor of the Journal of Approximation Theory.
Peter Kritzer is a Senior Scientist at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciencesin Linz, Austria, where he leads a work group doing research on quasi-Monte Carlo methods, multivariate algorithms, and Information-Based Complexity. Peter Kritzer's research focuses on mostly theoretical aspects of high-dimensional numerical integration, function approximation, and Information-Based Complexity. He has worked at Austrian and Australian universities and research institutions and has been awarded several prizes, such as the Information-Based Complexity Young Researcher Award, the Prize for Achievements in Information-Based Complexity, and the Christian Doppler Award. Apart from his research work at the Austrian Academy of Sciences, he teaches at Johannes Kepler University Linz and serves as an editorial board member of the Journal of Complexity.



Friedrich Pillichshammer is an Associate Professor in the Institute for Financial Mathematics and Applied Number Theory at the Johannes Kepler University Linz, Austria. He is an author with Josef Dick of the book"Digital