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.

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.