Hadamard invertibility of linearly recursive sequences in several variables
✍ Scribed by Earl J. Taft
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 251 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
A linearly recursive sequence in n variables is a tableau of scalars {./i,...i,,) for i 1 , i 2 ..... i, ~> 0. such that for each 1 <<.i<~n, all rows parallel to the ith axis satisfy a fixed linearly recursive relation hi(x ) with constant coefficients. We show that such a tableau is Hadamard invertible (i.e., the tableau (l/fi,...i,) is linearly recursive) if and only if all fi, ..i, ¢0, and each row is eventually an interlacing of geometric sequences. The procedure is effective, i.e., given a linearly recursive sequence.f= (.~,...i,), it can be tested for Hadamard invertibility by a finite algorithm. These results extend the case n = 1 of Larson and Taft.