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The two compact support wavelets respectively have a specified order of vanishing moments and a high degree of regularity.
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Though sparse, the arising system of linear equations is ill-conditioned; however, when written in terms of a short support wavelet basis with a well-chosen normalization, the resulting system, which is symmetric positive definite, appears to be well-conditioned, as evidenced by the fast convergence of the conjugate gradient iteration.
The analysis employs smooth wavelets and compactly supported wavelets.
Next, a method is proposed to design semi-orthogonal wavelets that are usually infinitely supported wavelets.
Compactly supported wavelets certainly satisfy condition (mathcal{M}^{1}) and thus Theorem 4.1 can be applied to all compactly supported wavelet bi-frames.
Compactly supported wavelets certainly satisfy condition (mathcal{M}) and thus Theorem 3.3 can be applied to all compactly supported orthogonal wavelets.
The displacement and force variables in the governing differential equation are approximated using Daubechies compactly supported wavelets.
They are obtained from Daubechies′ compactly supported wavelets which are restricted to the interval following an idea by Y. Meyer and then, suitably modified.
In this paper, we propose a generalized wavelet-Galerkin method based on the compactly supported wavelets, which is computationally very efficient even for differential equations with non-constant coefficients, no matter linear or nonlinear problems.
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets, their derivatives as well as some known coefficients in considered differential equations.
In [62] Hardin writes: "...compactly supported refinable functions (and thus compactly supported wavelets) are piecewise fractal interpolation functions.
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