Fast wavelet transforms and numerical algorithms I

作者：Gregory Beylkin, Ronald R. Coifman, Vladimir Abramovich Rokhlin · 发表于：Communications on Pure and Applied Mathematics · 年份：1991 · DOI：10.1002/cpa.3160440202 · 被引用次数：1785 · 研究领域：Image and Signal Denoising Methods、Mathematical Analysis and Transform Methods、Advanced Numerical Analysis Techniques

Abstract A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon‐Zygmund and pseudo‐differential operators. The algorithms of this paper require order O ( N ) or O ( N log N ) operations to apply an N × N matrix to a vector (depending on the particular operator and the version of the algorithm being used), and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here.