الفهرس الالي للمكتبة المركزية بجامعة عبد الحميد بن باديس - مستغانم
Titre : |
Wavelets and their application for the solution of partial differential equations in physics |
Type de document : |
texte imprimé |
Auteurs : |
S. Goedecker |
Mention d'édition : |
1re éd. |
Editeur : |
Lausanne : Presses polytechniques et universitaires romandes |
Année de publication : |
1998 |
Importance : |
72 p. |
Présentation : |
ill. |
Format : |
21 cm |
ISBN/ISSN/EAN : |
2-88074-398-2 |
Résumé : |
Based on a postgraduate course given by the author at the EPFL in January and February 1998, this book is intended to make the theory of wavelets understandable to the widest possible audience. In addition to a self-contained and intuitive presentation of the theory of wavelets, this book contains extensive tables with the basic filter coefficients of differential operators in several wavelet families. Anyone wishing to do so should be able to solve partial differential equations numerically in physics, chemistry or engineering using wavelets. Wavelets are a base set with extraordinary properties for the solution of differential equations. Their flexibility and efficiency allows us to deal with problems which are difficult, or even impossible, to resolve with conventional methods. It is expected that the theory of wavelets will soon become part of science and engineering curricula in the same way that Fourier analysis is nowadays.
Sommaire
Wavelets, an optimal basis set
A first tour of some wavelet families
Forming a basis set
The Haar wavelet
The concept of Multi-Resolution Analysis
The fast wavelet transform
How to plot wavelets
Interpretation of a wavelet spectrum
Interpolating wavelets
Expanding polynomials in a wavelet basis
Orthogonal versus biorthogonal wavelets
Expanding functions in a wavelet basis
Dynamic versus static data compression
Expanding nonuniform data in wavelets
Lifted wavelets
Second generation wavelets
Wavelet based smoothing of a function
The Fourier spectrum of wavelets
Wavelets in 2 and 3 dimensions
Wavelet grids in higher dimensions
The standard operator form
The non-standard operator form
Calculation of differential operators
Differential operators in higher dimensions
Transforming between wavelet families
Scalar products
The solution of Poisson's equation
The solution of Schrödinger's equation
Efficient implementation of filter operations
Outlook and conclusions |
Wavelets and their application for the solution of partial differential equations in physics [texte imprimé] / S. Goedecker . - 1re éd. . - Lausanne : Presses polytechniques et universitaires romandes, 1998 . - 72 p. : ill. ; 21 cm. ISBN : 2-88074-398-2
Résumé : |
Based on a postgraduate course given by the author at the EPFL in January and February 1998, this book is intended to make the theory of wavelets understandable to the widest possible audience. In addition to a self-contained and intuitive presentation of the theory of wavelets, this book contains extensive tables with the basic filter coefficients of differential operators in several wavelet families. Anyone wishing to do so should be able to solve partial differential equations numerically in physics, chemistry or engineering using wavelets. Wavelets are a base set with extraordinary properties for the solution of differential equations. Their flexibility and efficiency allows us to deal with problems which are difficult, or even impossible, to resolve with conventional methods. It is expected that the theory of wavelets will soon become part of science and engineering curricula in the same way that Fourier analysis is nowadays.
Sommaire
Wavelets, an optimal basis set
A first tour of some wavelet families
Forming a basis set
The Haar wavelet
The concept of Multi-Resolution Analysis
The fast wavelet transform
How to plot wavelets
Interpretation of a wavelet spectrum
Interpolating wavelets
Expanding polynomials in a wavelet basis
Orthogonal versus biorthogonal wavelets
Expanding functions in a wavelet basis
Dynamic versus static data compression
Expanding nonuniform data in wavelets
Lifted wavelets
Second generation wavelets
Wavelet based smoothing of a function
The Fourier spectrum of wavelets
Wavelets in 2 and 3 dimensions
Wavelet grids in higher dimensions
The standard operator form
The non-standard operator form
Calculation of differential operators
Differential operators in higher dimensions
Transforming between wavelet families
Scalar products
The solution of Poisson's equation
The solution of Schrödinger's equation
Efficient implementation of filter operations
Outlook and conclusions |
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