Wavelets In Numerical Simulation
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Wavelets In Numerical Simulation
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Author : Karsten Urban
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wavelets In Numerical Simulation written by Karsten Urban 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 2012-12-06 with Mathematics categories.
Sapere aude! Immanuel Kant (1724-1804) Numerical simulations playa key role in many areas of modern science and technology. They are necessary in particular when experiments for the underlying problem are too dangerous, too expensive or not even possible. The latter situation appears for example when relevant length scales are below the observation level. Moreover, numerical simulations are needed to control complex processes and systems. In all these cases the relevant problems may become highly complex. Hence the following issues are of vital importance for a numerical simulation: - Efficiency of the numerical solvers: Efficient and fast numerical schemes are the basis for a simulation of 'real world' problems. This becomes even more important for realtime problems where the runtime of the numerical simulation has to be of the order of the time span required by the simulated process. Without efficient solution methods the simulation of many problems is not feasible. 'Efficient' means here that the overall cost of the numerical scheme remains proportional to the degrees of freedom, i. e. , the numerical approximation is determined in linear time when the problem size grows e. g. to upgrade accuracy. Of course, as soon as the solution of large systems of equations is involved this requirement is very demanding.
Numerical Analysis Of Wavelet Methods
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Author : A. Cohen
language : en
Publisher: Elsevier
Release Date : 2003-04-29
Numerical Analysis Of Wavelet Methods written by A. Cohen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-29 with Mathematics categories.
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.
Wavelet Analysis And Applications
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Author : Tao Qian
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-24
Wavelet Analysis And Applications written by Tao Qian 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 2007-02-24 with Mathematics categories.
This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Numerical Analysis Of Wavelet Methods
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Author : Albert Cohen
language : en
Publisher: JAI Press
Release Date : 2003-06-26
Numerical Analysis Of Wavelet Methods written by Albert Cohen and has been published by JAI Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with categories.
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods: function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations: multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.
Computational Signal Processing With Wavelets
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Author : Anthony Teolis
language : en
Publisher: Birkhäuser
Release Date : 2017-10-02
Computational Signal Processing With Wavelets written by Anthony Teolis and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.
This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web. Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient "overcomplete" wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools. The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic...is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology
Wavelet Analysis And Applications
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Author : Peter Roberts
language : en
Publisher: New Age International
Release Date : 2007
Wavelet Analysis And Applications written by Peter Roberts and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Wavelets (Mathematics) categories.
Wavelets And Related Functions Constitute A Most Recent Set Of Mathematical Tools, Impacting Many Branches Of Mathematical And Applied Sciences, Ranging From Approximation Theory And Harmonic Analysis To Signal Analysis And Image Compression.This Volume Includes Lectures Delivered At The Platinum Jubilee Workshop And Tenth Ramanujan Symposium, Pjwtrs-2003, On Wavelet Analysis, Conducted In March 2003. The Contents Cover A Variety Of Interesting Topics Like Wavelets As Approximation Tools, Connections With Filter Banks, The Bessel-Wavelet Transform, Relations With Partial Differential Equations Of Fluid Flow, Weyl Heisenberg Frames, Reconstruction Of Functions From Irregular Sampling And Various Applications, Particularly In Electrical Engineering. This Book Will Be Useful To Mathematicians, Computer And Electrical Engineers, Systems Analysts And Applied Scientists. The Level Can Be Graduate Engineer Or Post Graduate Student Of Mathematics.
Wavelets
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Author : Gordon Erlebacher
language : en
Publisher: Oxford University Press
Release Date : 1996-01-04
Wavelets written by Gordon Erlebacher and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-04 with Science categories.
Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window". They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.
Wavelets And Their Applications
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Author : Mei Kobayashi
language : en
Publisher: SIAM
Release Date : 1998-01-01
Wavelets And Their Applications written by Mei Kobayashi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
This collection of independent case studies demonstrates how wavelet techniques have been used to solve open problems and develop insight into the nature of the systems under study. Each case begins with a description of the problem and points to the specific properties of wavelets and techniques used for determining a solution. The cases range from a very simple wavelet-based technique for reducing noise in laboratory data to complex work on two-dimensional geographical data display conducted at the Earthquake Research Institute in Japan. One case study shows how wavelet analysis is used in the development of a Japanese text-to-speech system for personal computers and another presents new wavelet techniques developed for and applied to the study of atmospheric wind, turbulent fluid, and seismic acceleration data. Although calculus and some junior and senior mathematics courses for scientists and engineers will suffice, a solid background in undergraduate mathematics, particularly analysis and numerical analysis, and some familiarity with the basics of wavelets are helpful for reading this book.
An Introduction To Wavelet Analysis
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Author : David F. Walnut
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
An Introduction To Wavelet Analysis written by David F. Walnut 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 2013-12-11 with Computers categories.
This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.
Cole D T D Analyse Num Rique
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Author : Jeffrey Saltzman
language : en
Publisher:
Release Date : 1997*
Cole D T D Analyse Num Rique written by Jeffrey Saltzman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997* with categories.