论文标题
迈向1英寸的Daubechies小波评估
Towards 1ULP evaluation of Daubechies Wavelets
论文作者
论文摘要
我们提出算法以数值评估daubechies小波和缩放函数的相对精度高。这些算法完善了Daubechies和Lagarias的建议，以评估使用花纹的两尺度差异方程定义的功能；小心地在一个快速收敛的插室家族中进行选择，这些插入器有效地捕获了该功能中存在的所有平滑度，并且其错误术语允许小渐近常数。我们还能够有效地计算衍生物，尽管准确性降低了。 Boost软件库中提供了实现。
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.
