Mathematics of Computation

Author(s): W. Lawton; S. L. Lee; Zuowei Shen.
Journal: Math. Comp. 65 (1996), 723-737.
MSC (1991): Primary 41A15, 41A30, 15A54, 65D07, 65F30
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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

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.

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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

Ruichi Ashino and Makoto Kametani, A Lemma on Matrices and a Construction of Multi-wavelets, Math. Japonica (2) 45 (1997), 267-287. (English)

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