Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function

Authors

  • Daniela Roşca Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat321-740

Keywords:

dilation equation, scaling function, cascade algorithm, wavelets
Abstract views: 186

Abstract

We define a class of matrices which includes, under some natural assumptions, the matrices \(\mathbf{m}\left( 0\right)\), \(\mathbf{m}\left( 1\right)\) and \(T_{2N-1}\), which are the key matrices of the wavelets theory. The matrices of this class have the property that the eigenvalues of a product matrix are products of their eigenvalues. This property is used in establishing some sufficient conditions for the convergence of the cascade algorithm and some sufficient conditions for the continuity of the scaling function. We generalize here the particular results obtained by us in a previous paper.

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References

Daubechies, I. and Lagarias, J., Two-scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals, SIAM J. Math. Anal., 23, no. 4, pp. 1031-1079, 1992, https://doi.org/10.1137/0523059. DOI: https://doi.org/10.1137/0523059

Roşca, D., Some classes of matrices with applications in wavelet theory, in Mathemathical Analysis and Approximation Theory, Burg Verlag, pp. 233-242, 2002.

Strang, G. and Nguyen, T., Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996.

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Published

2003-02-01

How to Cite

Roşca, D. (2003). Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function. Rev. Anal. Numér. Théor. Approx., 32(1), 109–120. https://doi.org/10.33993/jnaat321-740

Issue

Vol. 32 No. 1 (2003)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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