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 Mathematics 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 Mathematics 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.
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.
Portugaliae Mathematica
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Author : Antonio Monteiro
language : en
Publisher:
Release Date : 2010
Portugaliae Mathematica written by Antonio Monteiro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Function Spaces Of Logarithmic Smoothness Embeddings And Characterizations
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Author : Óscar Domínguez
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13
Function Spaces Of Logarithmic Smoothness Embeddings And Characterizations written by Óscar Domínguez and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.
View the abstract.
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 Mathematics 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.
Theory Of Function Spaces Iv
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Author : Hans Triebel
language : en
Publisher: Springer Nature
Release Date : 2020-01-23
Theory Of Function Spaces Iv written by Hans Triebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".
Nonlinear Potential Theory On Metric Spaces
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Author : Anders Björn
language : en
Publisher: European Mathematical Society
Release Date : 2011
Nonlinear Potential Theory On Metric Spaces written by Anders Björn 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 2011 with Mathematics categories.
The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Aicke Hinrichs
language : en
Publisher: Springer Nature
Release Date : 2024-07-12
Monte Carlo And Quasi Monte Carlo Methods written by Aicke Hinrichs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-12 with Mathematics categories.
This book presents the refereed proceedings of the 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Linz, Austria, and organized by the Johannes Kepler University Linz and the Austrian Academy of Sciences, in July 2022. 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 highly active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, in particular arising in finance, statistics and computer graphics.