On the roots of Daubechies polynomials. (English) Zbl 1143.42039
The paper provides the estimate \({1\over 2p}\leq \left| y \right| \leq {1 \over 2}\) for a root \(y\) of a polynomial of degree \(p-1\) which appears from the construction of Daubechies orthogonal mother wavelet with two channel filter bank. For previous works on this topic see [N. M. Temme, Asymptotics and numerics of zeros of polynomials that are related to Daubechies wavelets. Appl. Comput. Harmon. Anal. 4, No. 4, 414–428 (1997; Zbl 0903.42016)] and [G. Strang, Wavelets from filter banks. Ainsworth, M. (ed.) et al., Wavelets, multilevel methods and elliptic PDEs. 7th EPSRC numerical analysis summer school, University of Leicester, Leicester, GB, July 8–19, 1996. Oxford: Clarendon Press. Numerical Mathematics and Scientific Computation. 161–211 (1997; Zbl 0888.65140)].
Reviewer: Vladimir V. Kisil (Leeds)
MSC:
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
65H05 | Numerical computation of solutions to single equations |
30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |