Towards 1ULP evaluation of Daubechies Wavelets
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Publication:6340494
arXiv2005.05424MaRDI QIDQ6340494
Nicholas Thompson, George Ostrouchov, David Pugmire, Jeremy Logan, John Maddock, Scott Klasky
Publication date: 11 May 2020
Abstract: 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.
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