We give asymptotic approximations of the zeros of certain high degree polynomials. The zeros can be used to compute the filter coefficients in the dilation equations which define the compactly supported orthogonal Daubechies wavelets. Computational schemes are presented to obtain the numerical values of the zeros within high precision.

Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (msc 33B20), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Computation of special functions, construction of tables (msc 65D20)
CWI
Department of Analysis, Algebra and Geometry [AM]
Computational Dynamics

Temme, N.M. (1996). Asymptotics and numerics of zeros of polynomials that are related to Daubechies wavelets. Department of Analysis, Algebra and Geometry [AM]. CWI.