Trigonometric wavelets for Hermite interpolation
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A multiresolution analysis of nested subspaces of trigonometric polynomials of Hermite interpolation on a dyadic partition of nodes on the interval [0,2π].Abstract:
The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0,2π]. Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.read more
Citations
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Galerkin trigonometric wavelet methods for the natural boundary integral equations
Wen-Sheng Chen,Wei Lin +1 more
TL;DR: It is proved that the stiffness matrix is a block diagonal matrix and its diagonal elements are some symmetric and block circulant submatrices.
Journal ArticleDOI
Finite element analysis of beam structures based on trigonometric wavelet
Wen-Yu He,Wei-Xin Ren +1 more
TL;DR: In this paper, a trigonometric wavelet finite beam element is formulated to carry out bending, free vibration and buckling of beam structures, which can deal with boundary conditions and connection between adjacent elements as the traditional finite element method does.
Journal ArticleDOI
Trigonometric Hermite wavelet approximation for the integral equations of second kind with weakly singular kernel
Jing Gao,Yao-Lin Jiang +1 more
TL;DR: In this article, a trigonometric Hermite wavelet Galerkin method for the Fredholm integral equation with weakly singular kernel was proposed. But the convergence analysis was not considered.
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The natural integral equations of plane elasticity problem and its wavelet methods
Youjian Shen,Wei Lin +1 more
TL;DR: Interpolatory Hermite-type trigonometric wavelet is applied to investigate the numerical solution of the natural boundary integral equation of plane elasticity problem by Galerkin method to find the approximate solution.
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Numerical solution of nth‐order integro‐differential equations using trigonometric wavelets
TL;DR: In this paper, the authors applied the trigonometric wavelets for the solution of the Fredholm integro-differential equations of nth-order and obtained an estimation of error bound for this method.
References
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Book
An introduction to wavelets
TL;DR: An Overview: From Fourier Analysis to Wavelet Analysis, Multiresolution Analysis, Splines, and Wavelets.
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An introduction to wavelets
TL;DR: The mathematics have been worked out in excruciating detail, and wavelet theory is now in the refinement stage, which involves generalizing and extending wavelets, such as in extending wavelet packet techniques.
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On compactly supported spline wavelets and a duality principle
Charles K. Chui,Jianzhong Wang +1 more
TL;DR: In this paper, a compactly supported basic wavelet ψ m (x) that generates corresponding orthogonal complementary wavelet subspaces was presented. And the two finite sequences that describe the two-scale relations of N m(x) and ψm (x), in terms of n m (2x−j), j∈Z, yield an efficient reconstruction algorithm.
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On trigonometric wavelets
TL;DR: In this article, wavelets in terms of sine and cosine functions are constructed for decomposing 2π-periodic square-integrable functions into different octaves and yielding local information within each octave.