On the Daubechies-based wavelet differentiation matrix

Cover of: On the Daubechies-based wavelet differentiation matrix |

Published by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va .

Written in English

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Subjects:

  • Wavelets (Mathematics),
  • Matrices.

Edition Notes

Book details

Other titlesOn the Daubechies based wavelet differentiation matrix.
StatementLeland Jameson.
SeriesICASE report -- no. 93-95., NASA contractor report -- 191583., NASA contractor report -- NASA CR-191583.
ContributionsLangley Research Center.
The Physical Object
FormatMicroform
Pagination1 v.
ID Numbers
Open LibraryOL15389060M

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The differentiation matrix for a Daubechies-based wavelet basis defined on an interval is constructed. It is shown that the differentiation matrix based on the currently available boundary construc Cited by: Get this from a library. On the Daubechies-based wavelet differentiation matrix.

[Leland Jameson; Langley Research Center.]. The Daubechies wavelet based differentiation matrix will be constructed for periodic boundary conditions. It will be proved that this matrix displays the very important property of superconvergence.

The relationship between Daubechies-based numerical methods and finite difference methods will be by: Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. On the Daubechies-based wavelet differentiation matrix in SearchWorks catalog Skip to search Skip to main content.

Get this from a library. On the differentiation matrix for Daubechies-based wavelets on an interval. [Leland Jameson; Langley Research Center.]. The differentiation matrix for a Daubechies-based wavelet basis defined on an interval is constructed. It is shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions.

Abstract. The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of.

Special fixed threshold for differentiation matrix a Diagonal matrix M N 15 Depth of wavelet decomposition Diffusion constant x 23 Substitution for or 25 Variable in Fourier transform Advection constant x 11, 13 Basic scaling function x jk 13 j k x k 13 x jk 6, 34 Periodized scaling function x 13 Basic wavelet x jk 13 j k x k.

Abstract. Wavelet applications to date have been dominated by signal and image processing. While perhaps not immediately appealing as a means of solving differential equations, the growing body of literature in this area indicates that wavelets have a role to play here, too.

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions. [6]. This understanding will be found through the differentiation matrix.

In [4] the differentiation matrix was found for Daubechies wavelets with periodic boundary conditions, and a very high On the Daubechies-based wavelet differentiation matrix book of differentiation accuracy known as superconver-gence was proven to exist.

Furthermore, it was seen that a Daubechies-based wavelet. This book gives scientists and engineers a On the Daubechies-based wavelet differentiation matrix book 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. The differentiation matrix for a spline-based wavelet basis without decomposition at multiple scales is constructed.

It is shown that regardless of the properties that one imposes on a spline basis, the differentiation matrix is always the one encountered when the basis is.

On the Daubechies-based wavelet differentiation matrix The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only.

In this research, a Bernoulli wavelet operational matrix of fractional integration is presented. Bernoulli wavelets and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving the fractional delay differential equations is.

Jameson, On the Daubechies-based wavelet differentiation matrix, Technical report, Institute for Computer Applications in Science and Engineering, NASA Langley, VA (). Google Scholar L. Jameson, On the wavelet optimized finite difference method, Technical report, Institute for Computer Applications in Science and Engineering, NASA.

The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature.

How else can one ex plain the remarkable effectiveness of mathematics in describing and predicting the physical world. The projection of the mathematical method onto the.

On the Spline-Based Wavelet Differentiation Matrix (Taiwanese Chinese) Paperback – January 1, by Leland Jameson (Author) See all formats and editions Hide other formats and editions. Price New from Used from Paperback "Please retry" $ $ $ PaperbackAuthor: Leland Jameson.

Daubechies-based visual table of contents Daubechies-based visual table of contents Rosiek, Mark R.; McLeod, Mark L. ABSTRACT Visual table of contents provides users with easier access to imagery databases. Reduced resolution images are collected in a portfolio, presented to the user to browse through and select an image based on this thumbnail image.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's. Hampton, Va.: [Springfield, Va: National Aeronautics and Space Administration, Langley Research Center ; National Technical Information Service, distributor.

MLA Citation. Cai, Wei. and Wang, Chien-chung. and Langley Research Center. An introduction to wavelet theory in finance [electronic resource]: a wavelet multiscale approach / Francis In, Sangbae Kim World Scientific Pub Singapore ; Hackensack, NJ Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required.

Jameson, "On the Spline-Based Wavelet Differentiation Matrix." L. Jameson, "On the Differention Matrix for Daubechies-Based Wavelets on an Interval." L. Jameson, "On the Daubechies-Based Wavelet Differentiation Matrix." L. Jameson, "On the Wavelet Optimized Finite Difference Method.".

The differentiation matrix for a Daubechies-based wavelet basis will be constructed and 'superconvergence' will be proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only.

The formulation and implementation of wavelet based methods for the solution of multi-dimensional partial differential equations in complex geometries is discussed.

Utilizing the close connection between Daubechies wavelets and finite difference methods on arbitrary grids, we formulate a wavelet based collocation method, well suited for dealing. Bernoulli wavelet expansions together with this operational matrix method, by taking suitable collocation points, converts the given Lane–Emden type equations into a system of algebraic equations.

Solution to the problem is identified by solving this system of equations. This study presents the results of grey-level co-occurrence matrix (GLCM) and wavelet transform (WT) texture analysis for forest and non-forest vegetation types differentiation in QuickBird imagery.

Using semivariogram fitting, the optimal GLCM windows for the land cover classes within the. This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling.

Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods.

Starting from the space-time angle and based on the traffic accident data, this article firstly carries out the wavelet decomposition of the incident data of time series to realize the problem optimization of sparse matrix and then studies the spatial differentiation pattern of traffic accidents through the k-means clustering method.

And under. Because the Daubechies wavelet family have implicit expression, analytical differentiation or integration of Daubechies wavelets is impossible. And thus, simpler wavelets, which are based on orthogonal polynomials, such as Haar, Gegenbauer, Legendre, Hermite and Chebyshev polynomials, are commonly used in wavelet-based numerical methods by many.

Wavelet analysis provides information on the energy present at various scales and locations throughout a computational domain. This information is precisely the information that is needed to define the appropriate gridpoint densities and the appropriate numerical order to resolve the physics at hand in the computationally most efficient manner.

Filter design for molecular factor computing using wavelet functions. Analytica Chimica Acta, DOI: / Yuanlu Li, Chang Pan, Xiao Meng, Yaqing Ding, Haixiu Chen. Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement.

As a mathematical subject, wavelet theory involves tools from a host of neighboring fields, functional and harmonic analysis, numerical analysis, mathematics of computation, and operator theory. Wavelets now serve as an alternative to classical Fourier methods, Fourier series and integrals.

In this paper, a wavelet numerical method for solving nonlinear Volterra integro-differential equations of fractional order is presented. The method is based upon Euler wavelet approximations. The Euler wavelet is first presented and an operational matrix of fractional-order integration is derived.

By using the operational matrix, the nonlinear fractional integro-differential equations are. Leland Jameson has written: 'On the spline-based wavelet differentiation matrix' -- subject(s): Wavelets (Mathematics), Matrices, Differentiation matrix, Wavelets 'On the wavelet optimized finite.

Wavelet Transformations and Their Applications in Chemistry pioneers a new approach to classifying existing chemometric techniques for data analysis in one and two dimensions, using a practical applications approach to illustrating chemical examples and problems.

Written in a simple, balanced, applications-based style, the book is geared to both theorists and non-mathematicians. This text. The new method is very straightforward. The numerical values of the matrix K are determined by wavelet analysis and are simply a function of the magnitude of the wavelet coefficients in the same area of the domain where the assimilation occurs.

In this manner, the wavelet analysis detects the areas of the domain where large computational errors occur and these areas will have relatively. The daubechies based wavelet is implemented in Java Media Framework (JMF) and runs under Intel, Xeon CPU ( GHz) machine with 8 GB of RAM.

The general flow of the experiments starts with the decomposition of data base image using D4 wavelet. provides + free mathematics eBooks, worksheets, shortcuts, formulas and question with solution. In this paper, we propose an image splicing detecting method using the characteristic function moments for the inter-scale co-occurrence matrix in the wavelet domain.

We construct the co-occurrence matrices by using a pair of wavelet difference values across inter-scale wavelet subbands. In this process, we do not adopt the thresholding operation to prevent information loss. The toolbox also includes apps and functions for decimated and nondecimated discrete wavelet analysis of signals and images, including wavelet packets and dual-tree transforms.

Using continuous wavelet analysis, you can explore how spectral features evolve over time, identify common time-varying patterns in two signals, and perform time. A procedure for determining the current parameters of the oscillator is based on the calculation of the wavelet coefficients of the signal system using fast discrete wavelet transform and application of the differentiation formulas wavelet expansions.

This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions.

The use of wavelet analysis describes the pattern, trends, and the structures that might be overlooked in the raw data. The usefulness of wavelets in data analysis is very clear, particularly in the field of statistics, where large and cumbersome data sets are prevalent.

Wavelet analysis is .

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