Bases In Function Spaces Sampling Discrepancy Numerical Integration
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Bases In Function Spaces Sampling Discrepancy Numerical Integration
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Author : Hans Triebel
language : en
Publisher: European Mathematical Society
Release Date : 2010
Bases In Function Spaces Sampling Discrepancy Numerical Integration written by Hans Triebel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Fuction spaces categories.
The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean $n$-space and $n$-cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).
Faber Systems And Their Use In Sampling Discrepancy Numerical Integration
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Author : Hans Triebel
language : en
Publisher: European Mathematical Society
Release Date : 2012
Faber Systems And Their Use In Sampling Discrepancy Numerical Integration written by Hans Triebel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Function spaces categories.
This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, ``Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration'' (EMS, 2010), from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.
Faber Systems And Their Use In Sampling Discrepancy Numerical Integration
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Author : Hans Triebel
language : en
Publisher:
Release Date :
Faber Systems And Their Use In Sampling Discrepancy Numerical Integration written by Hans Triebel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Function spaces categories.
This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration (EMS, 2010) from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory.
Monte Carlo And Quasi Monte Carlo Methods 2010
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Author : Leszek Plaskota
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-23
Monte Carlo And Quasi Monte Carlo Methods 2010 written by Leszek Plaskota and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-23 with Mathematics categories.
This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. 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. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Ronald Cools
language : en
Publisher: Springer
Release Date : 2016-06-13
Monte Carlo And Quasi Monte Carlo Methods written by Ronald Cools and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-13 with Mathematics categories.
This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. 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 and computer graphics.
A Panorama Of Discrepancy Theory
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Author : William Chen
language : en
Publisher: Springer
Release Date : 2014-10-07
A Panorama Of Discrepancy Theory written by William Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Mathematics categories.
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.
Efficient Numerical Methods For Non Local Operators
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Author : Steffen Börm
language : en
Publisher: European Mathematical Society
Release Date : 2010
Efficient Numerical Methods For Non Local Operators written by Steffen Börm and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Matrices categories.
Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense $n\times n$ matrix in standard representation requires $n^2$ units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only $O(n k \log n)$ units of storage, where $k$ is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions, and to solve matrix equations used in control theory. $\mathcal{H}^2$-matrices offer a refinement of hierarchical matrices: Using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This book gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of $\mathcal{H}^2$-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are required only in isolated sections, e.g., for certain classes of model problems.
Monte Carlo And Quasi Monte Carlo Methods 2012
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Author : Josef Dick
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-05
Monte Carlo And Quasi Monte Carlo Methods 2012 written by Josef Dick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-05 with Mathematics categories.
This book represents the refereed proceedings of the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of New South Wales (Australia) in February 2012. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. 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. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance, statistics and computer graphics.
Digital Nets And Sequences
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Author : Josef Dick
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-09
Digital Nets And Sequences written by Josef Dick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Computers categories.
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.
Multivariate Approximation
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Author : V. Temlyakov
language : en
Publisher: Cambridge University Press
Release Date : 2018-07-19
Multivariate Approximation written by V. Temlyakov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Computers categories.
Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.