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 wi
Highlighting the new aspects of MATLAB® 7.10 and expanding on many existing features, MATLAB® Primer, Eighth Edition shows you how to solve problems in science, engineering, and mathematics. N
Donald Knuth’s influence in computer science ranges from the invention of methods for translating and defining programming languages to the creation of the TEX and METAFONT systems for desktop publish
Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those method
Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theor
The LLL algorithm is a polynomial-time lattice reduction algorithm, named after its inventors, Arjen Lenstra, Hendrik Lenstra and Laszlo Lovasz. The algorithm has revolutionized computational aspects
A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accura
Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density fun
Explores the Impact of the Analysis of Algorithms on Many Areas within and beyond Computer ScienceA flexible, interactive teaching format enhanced by a large selection of examples and exercisesDevelop
Comprehensive Coverage of the New, Easy-to-Learn C#Although C, C++, Java, and Fortran are well-established programming languages, the relatively new C# is much easier to use for solving complex scient
Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical
These are the proceedings of the 18th international conference on domain decomposition methods in science and engineering, held?in Jerusalem, January 12-17, 2008. Domain decomposition methods are iter
Classroom-tested and teacher approved, these activities help children ages three to six learn all about numbers. With one hundred engaging and fun activities, Learn Every Day About Numbers offers ever
Numerical and Analytical Methods with MATLABR presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve sy
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical l
Recent Advances in Numerical Methods features contributions from distinguished researchers, focused on significant aspects of current numerical methods and computational mathematics. The increasing n
Written for undergraduate and graduate students in math, applied math, computer science, and engineering, this book stresses the connections between the theoretical nature of mathematical objects and
Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff–Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff–Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It co
Finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of PDEs. This book is a thorough yet concise guide to the theory and prac
