1 research outputs found
Towards 1ULP evaluation of Daubechies Wavelets
We present algorithms to numerically evaluate Daubechies wavelets and scaling
functions to high relative accuracy. These algorithms refine the suggestion of
Daubechies and Lagarias to evaluate functions defined by two-scale difference
equations using splines; carefully choosing amongst a family of rapidly
convergent interpolators which effectively capture all the smoothness present
in the function and whose error term admits a small asymptotic constant. We are
also able to efficiently compute derivatives, though with a smoothness-induced
reduction in accuracy. An implementation is provided in the Boost Software
Library.Comment: 16 pages, 5 figure