A Panorama of Discrepancy Theory

A Panorama of Discrepancy Theory
Title A Panorama of Discrepancy Theory PDF eBook
Author William Chen
Publisher Springer
Pages 708
Release 2014-10-07
Genre Mathematics
ISBN 3319046969

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This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.

Discrepancy Theory

Discrepancy Theory
Title Discrepancy Theory PDF eBook
Author Dmitriy Bilyk
Publisher Walter de Gruyter GmbH & Co KG
Pages 225
Release 2020-01-20
Genre Mathematics
ISBN 3110652587

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The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

Number Theory, Fourier Analysis and Geometric Discrepancy

Number Theory, Fourier Analysis and Geometric Discrepancy
Title Number Theory, Fourier Analysis and Geometric Discrepancy PDF eBook
Author Giancarlo Travaglini
Publisher Cambridge University Press
Pages 251
Release 2014-06-12
Genre Mathematics
ISBN 1107044030

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Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

Handbook of Discrete and Computational Geometry

Handbook of Discrete and Computational Geometry
Title Handbook of Discrete and Computational Geometry PDF eBook
Author Csaba D. Toth
Publisher CRC Press
Pages 2354
Release 2017-11-22
Genre Computers
ISBN 1351645919

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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Monte Carlo and Quasi-Monte Carlo Methods

Monte Carlo and Quasi-Monte Carlo Methods
Title Monte Carlo and Quasi-Monte Carlo Methods PDF eBook
Author Art B. Owen
Publisher Springer
Pages 476
Release 2018-07-03
Genre Computers
ISBN 3319914367

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This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Introduction to Quasi-Monte Carlo Integration and Applications

Introduction to Quasi-Monte Carlo Integration and Applications
Title Introduction to Quasi-Monte Carlo Integration and Applications PDF eBook
Author Gunther Leobacher
Publisher Springer
Pages 206
Release 2014-09-12
Genre Mathematics
ISBN 3319034251

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This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems. Each chapter closes with suggestions for further reading and with exercises which help students to arrive at a deeper understanding of the material presented. The book is based on a one-semester, two-hour undergraduate course and is well-suited for readers with a basic grasp of algebra, calculus, linear algebra and basic probability theory. It provides an accessible introduction for undergraduate students in mathematics or computer science.

Lattice Rules

Lattice Rules
Title Lattice Rules PDF eBook
Author Josef Dick
Publisher Springer Nature
Pages 584
Release 2022-08-24
Genre Mathematics
ISBN 3031099516

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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.