Lexing Ying

TL;DR: This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface by applying the recently developed phase flow method, an efficient and accurate technique for constructing phase maps for nonlinear ordinary differential equations on invariant manifolds, which are here the unit tangent bundles of the surfaces under study.

TL;DR: It is proved that the synchrosqueezed wave packet transform identifies these components and estimates their local wavevectors for a function that is a superposition of several wave-like components with a highly oscillatory pattern satisfying certain separation conditions.

TL;DR: This work first represents the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network.

TL;DR: The butterfly factorization as mentioned in this paper is a data-sparse approximation for the matrices that satisfy a complementary low-rank property, which can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually.

TL;DR: In this article, a fast algorithm for computing sparse Fourier transforms with spatial and Fourier data supported on curves or surfaces is proposed. But this algorithm is based on the butterfly algorithm.