Displaying similar documents to “Daubechies wavelets on intervals with application to BVPs”

Quadrature formulas based on the scaling function

Václav Finěk (2005)

Applications of Mathematics

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The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M 2 = M 1 2 and M 0 = 1 . So, in this sense, its choice is optimal. Numerical examples are given.

On the computation of scaling coefficients of Daubechies' wavelets

Dana Černá, Václav Finěk (2004)

Open Mathematics

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In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.

Approximation properties of wavelets and relations among scaling moments II

Václav Finěk (2004)

Open Mathematics

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A new orthonormality condition for scaling functions is derived. This condition shows a close connection between orthonormality and relations among discrete scaling moments. This new condition in connection with certain approximation properties of scaling functions enables to prove new relations among discrete scaling moments and consequently the same relations for continuous scaling moments.

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.