Numerical Analysis of Wavelet Methods

Author: A. Cohen
Publisher: Elsevier
ISBN: 9780080537856
Format: PDF, ePub, Docs
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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.

Isogeometric Analysis and Applications 2014

Author: Bert Jüttler
Publisher: Springer
ISBN: 3319233157
Format: PDF, Kindle
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Isogeometric Analysis is a groundbreaking computational approach that promises the possibility of integrating the finite element method into conventional spline-based CAD design tools. It thus bridges the gap between numerical analysis and geometry, and moreover it allows to tackle new cutting edge applications at the frontiers of research in science and engineering. This proceedings volume contains a selection of outstanding research papers presented at the second International Workshop on Isogeometric Analysis and Applications, held at Annweiler, Germany, in April 2014.

150 Years of Mathematics at Washington University in St Louis

Author: Gary R. Jensen
Publisher: American Mathematical Soc.
ISBN: 082183603X
Format: PDF, Mobi
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Articles in this book cover a wide range of important topics in mathematics, and are based on talks given at the conference commemorating the 150th anniversary of Washington University in St. Louis. The volume is prefaced by a brief history of the Washington University Department of Mathematics, a roster of those who received the PhD degree from the department, and a list of the Washington University Department of Mathematics faculty since the founding of the university.

Wavelets and Multiwavelets

Author: Fritz Keinert
Publisher: CRC Press
ISBN: 0203011597
Format: PDF, ePub, Mobi
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Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. Meeting the needs of engineers and mathematicians, this book provides a comprehensive overview of multiwavelets. The author presents the theory of wavelets from the viewpoint of general multiwavelets, which includes scalar m-band and standard wavelets as special cases, provides a more coherent approach, and provides alternative proofs and new insights even for standard wavelets. The treatment includes complete MATLAB routines that allow readers to implement and experiment with multiwavelet algorithms.

Wavelets and Their Applications

Author: Mei Kobayashi
Publisher: SIAM
ISBN: 9781611971385
Format: PDF, ePub, Docs
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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.

Multiscale Wavelet Methods for Partial Differential Equations

Author: Wolfgang Dahmen
Publisher: Elsevier
ISBN: 9780080537146
Format: PDF, ePub, Docs
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This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Covers important areas of computational mechanics such as elasticity and computational fluid dynamics Includes a clear study of turbulence modeling Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications

Wavelet Methods in Mathematical Analysis and Engineering

Author: Alain Damlamian
Publisher: World Scientific
ISBN: 9814322865
Format: PDF, ePub, Docs
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This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.

Applied Functional Analysis

Author: Abul Hasan Siddiqi
Publisher: CRC Press
ISBN: 0824756622
Format: PDF, ePub
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The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.

Wavelet Theory and Its Applications

Author: Randy K. Young
Publisher: Springer Science & Business Media
ISBN: 1461535840
Format: PDF, Kindle
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The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.