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Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.

Monte Carlo method. --- Nets (Mathematics) --- Sequences (Mathematics) --- Numerical integration. --- Digital filters (Mathematics) --- Data smoothing filters --- Filters, Digital (Mathematics) --- Linear digital filters (Mathematics) --- Linear filters (Mathematics) --- Numerical filters --- Smoothing filters (Mathematics) --- Digital electronics --- Filters (Mathematics) --- Fourier transformations --- Functional analysis --- Numerical analysis --- Numerical calculations --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Moore-Smith convergence --- Net equations --- Net methods (Mathematics) --- Convergence --- Set theory --- Topology --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Stochastic processes

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Asymptotic Wave Theory

Mathematical physics --- Electromagnetism. Ferromagnetism --- Differential equations --- Initial value problems --- Équations différentielles. --- Problèmes aux valeurs initiales. --- Développements asymptotiques --- Col, Méthode du --- Asymptotic expansions --- Method of steepest descent (Numerical analysis) --- Numerical integration --- Problèmes aux valeurs initiales --- Intégration numérique --- Wave-motion, Theory of. --- Wave equation. --- Asymptotic expansions. --- Initial value problems. --- Numerical integration. --- Wave equations --- Asymptotic theory. --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis --- Differential equations, Partial --- Wave-motion, Theory of --- Undulatory theory --- Mechanics --- 519.6 --- 681.3*G17 --- 681.3 *G18 --- 532 --- 532 Fluid mechanics in general. Mechanics of liquids (hydromechanics) --- Fluid mechanics in general. Mechanics of liquids (hydromechanics) --- Développements asymptotiques --- Col, Méthode du --- Ondes --- Propagation --- Differential equations. --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Problems, Initial value --- Boundary value problems --- Analyse numerique --- Equations differentielles ordinaires --- Equations differentielles --- Methodes numeriques --- Equations aux derivees partielles hyperboliques --- Transformation de laplace --- Geophysique --- Geodynamique --- Seismologie