Lattice Rules: Numerical Integration, Approximation, and Discrepancy
Josef Dick, Peter Kritzer, Friedrich Pillichshammer, 978-3-031-09951-9, 978-3-031-09950-2, 3031099508, 978-3031099502, 9783031099502, 3031099532, 978-3031099533, 9783031099533
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.