A dual‐space multilevel kernel‐splitting framework for discrete and continuous convolution

• Published in: Communications on pure and applied mathematics Vol. 78; no. 5; pp. 1086 - 1143
• Main Authors: Jiang, Shidong, Greengard, Leslie
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.05.2025
• Subjects: Approximation; Asymptotic methods; Computation; Fourier transforms; Green's functions; Machine learning; Multilevel; Multipoles; Partial differential equations; Radial basis function; Splitting; Telescoping; Tensors
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.22240

We introduce a new class of multilevel, adaptive, dual‐space methods for computing fast convolutional transformations. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential equations (PDEs) to power functions and radial basis fun...