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, 2014 This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral ...
Ülo Lepik, Helle Hein
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Solving PDEs with the aid of two-dimensional Haar wavelets
Computers and Mathematics With Applications, 2011 Two-dimensional Haar wavelets are applied for solution of the partial differential equations (PDEs). The proposed method is mathematically simple and fast.
U Lepik
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Crystallographic Haar Wavelets
Journal of Fourier Analysis and Applications, 2011Let \(\Gamma\) be a \(d\)-dimensional crystallographic group and let \(a:\,{\mathbb R}^d \to {\mathbb R}^d\) be an expanding affine map. By definition, \((\Gamma,a)\)-crystallographic multiwavelets form a finite set of functions \(\{\psi^1,\ldots, \psi^L\}\), which generate an orthonormal basis, a Riesz basis or a Parseval frame for \(L^1({\mathbb R}^d)
González, Alfredo L. +1 more
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Journal of Interdisciplinary Mathematics, 2001
Abstract In this paper is discussed the numerical approximation of differential operators using Haar wavelet bases and their spline-derivatives. It is shown how to smooth the Haar family of wavelets using splines, and to compute the derivatives of the Haar function using the splines.
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Abstract In this paper is discussed the numerical approximation of differential operators using Haar wavelet bases and their spline-derivatives. It is shown how to smooth the Haar family of wavelets using splines, and to compute the derivatives of the Haar function using the splines.
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Applied Mathematics and Computation, 2004
The authors give a detailed description of the Haar wavelet transform associated with non-uniform partitions of the real line. Algorithms for decomposition and reconstruction are studied.
François Dubeau +2 more
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The authors give a detailed description of the Haar wavelet transform associated with non-uniform partitions of the real line. Algorithms for decomposition and reconstruction are studied.
François Dubeau +2 more
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Wavelets in Generalized Haar Spaces
Journal of Mathematical Sciences, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Journal of Physics A: Mathematical and General, 1996
Summary: We construct a new type of Haar wavelets, called \(\tau\)-wavelets of Haar, using the arithmetics of the solutions \(\tau=\frac 12 (1+\sqrt{5})\) and \(\sigma=\frac 12 (1-\sqrt{5})\) of the algebraic equation \(x^2=x+1\).
Gazeau, J.-P., Patera, J.
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Summary: We construct a new type of Haar wavelets, called \(\tau\)-wavelets of Haar, using the arithmetics of the solutions \(\tau=\frac 12 (1+\sqrt{5})\) and \(\sigma=\frac 12 (1-\sqrt{5})\) of the algebraic equation \(x^2=x+1\).
Gazeau, J.-P., Patera, J.
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The Haar wavelets operational matrix of integration
International Journal of Systems Science, 1996The Haar wavelets operational matrix of integration P is derived, which is similar to those previously derived for other types of orthogonal functions such as Walsh, block-pulse, Laguerre, Legendre and Chebyshev. A general procedure of forming this matrix P is summarized.
Jin-Sheng Guf, Wei-Sun Jiang
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Int-Haar: Improving Precision of the Haar Interval Wavelet Extension
2013 2nd Workshop-School on Theoretical Computer Science, 2013This work describes the interval extension of the Haar Wavelet Transform (HWT), implemented with C-XSC, being the first step on the development of the Int-DWTs library, which will provide interval results for several Discrete Wavelet Transforms (DWTs).
Vinicius R. dos Santos +3 more
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Application of Haar Wavelets on Medical Images
Journal of Electronic Commerce in Organizations, 2015Recently, the information processing approaches are increased. These methods can be used for several purposes: compressing, restoring, and information encoding. The raw data are less presented and are gradually replaced by others formats in terms of space or speed of access.
Rachid El Ayachi +2 more
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