Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function
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...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2003-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/740 |
| _version_ | 1811291495630635008 |
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| author | Daniela Roşca |
| author_facet | Daniela Roşca |
| author_sort | Daniela Roşca |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T04:30:17Z |
| format | Article |
| id | doaj.art-35b017d21d344e0bab9b2313f242b2ad |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-13T04:30:17Z |
| publishDate | 2003-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-35b017d21d344e0bab9b2313f242b2ad2022-12-22T03:02:21ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2003-02-01321Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling functionDaniela Roşca0Technical University of Cluj-Napoca, RomaniaWe 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.https://ictp.acad.ro/jnaat/journal/article/view/740dilation equationscaling functioncascade algorithmwavelets |
| spellingShingle | Daniela Roşca Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function Journal of Numerical Analysis and Approximation Theory dilation equation scaling function cascade algorithm wavelets |
| title | Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| title_full | Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| title_fullStr | Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| title_full_unstemmed | Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| title_short | Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| title_sort | some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function |
| topic | dilation equation scaling function cascade algorithm wavelets |
| url | https://ictp.acad.ro/jnaat/journal/article/view/740 |
| work_keys_str_mv | AT danielarosca somesufficientconditionsfortheconvergenceofthecascadealgorithmandforthecontinuityofthescalingfunction |