An algorithm for matrix extension and wavelet construction
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- by W. Lawton, S. L. Lee and Zuowei Shen PDF
- Math. Comp. 65 (1996), 723-737 Request permission
Abstract:
This paper gives a practical method of extending an $n\times r$ matrix $P(z)$, $r \leq n$, with Laurent polynomial entries in one complex variable $z$, to a square matrix also with Laurent polynomial entries. If $P(z)$ has orthonormal columns when $z$ is restricted to the torus $\mathbf {T}$, it can be extended to a paraunitary matrix. If $P(z)$ has rank $r$ for each $z\in \mathbf {T}$, it can be extended to a matrix with nonvanishing determinant on $\mathbf {T}$. The method is easily implemented in the computer. It is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter.References
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Additional Information
- W. Lawton
- Affiliation: Institute of Systems Science, National University of Singapore, Heng Mui Keng Terrace, Kent Ridge, Singapore 0511
- Email: wlawton@iss.nus.sg
- S. L. Lee
- Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
- Email: matleesl@math.nus.sg
- Zuowei Shen
- MR Author ID: 292105
- Email: matzuows@math.nus.sg
- Received by editor(s): February 15, 1994
- Received by editor(s) in revised form: October 4, 1994, and January 30, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 723-737
- MSC (1991): Primary 41A15, 41A30, 15A54, 65D07, 65F30
- DOI: https://doi.org/10.1090/S0025-5718-96-00714-4
- MathSciNet review: 1333319