Browsing by Author "Ying, L"
Now showing items 115 of 15

A fast algorithm for multilinear operators
Yang, H; Ying, L (Applied and Computational Harmonic Analysis, 2012)This paper introduces a fast algorithm for computing multilinear integrals which are defined through Fourier multipliers. The algorithm is based on generating a hierarchical decomposition of the summation domain into squares, ... 
A multiscale butterfly algorithm for multidimensional fourier integral operators
Li, Y; Yang, H; Ying, L (Multiscale Modeling and Simulation, 20150101)© 2015 Society for Industrial and Applied Mathematics.This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) =∫ <inf>ℝ d</inf>a(x, ξ)e2πiΦ(x,ξ)f(ξ)dξ, ... 
Adaptive local basis set for KohnSham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Lin, L; Lu, J; Ying, L; E, W (Journal of Computational Physics, 20120220)KohnSham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the KohnSham Hamiltonian generally results in a large number ... 
Butterfly factorization
Li, Y; Yang, H; Martin, ER; Ho, KL; Ying, L (Multiscale Modeling and Simulation, 20150101)© 2015 Society for Industrial and Applied Mathematics.The paper introduces the butterfly factorization as a datasparse approximation for the matrices that satisfy a complementary lowrank property. The factorization can ... 
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
Lu, J; Ying, L (Journal of Computational Physics, 20151201)© 2015 Elsevier Inc.Electron repulsion integral tensor has ubiquitous applications in electronic structure computations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor ... 
Crystal image analysis using 2D synchrosqueezed transforms
Yang, H; Lu, J; Ying, L (Multiscale Modeling and Simulation, 20150101)© 2015 Society for Industrial and Applied Mathematics.We propose efficient algorithms based on a bandlimited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal ... 
Fast construction of hierarchical matrix representation from matrixvector multiplication
Lin, L; Lu, J; Ying, L (Journal of Computational Physics, 20110510)We develop a hierarchical matrix construction algorithm using matrixvector multiplications, based on the randomized singular value decomposition of lowrank matrices. The algorithm uses O(logn) applications of the matrix ... 
Multidimensional Butterfly Factorization
Li, Y; Yang, H; Ying, L 
Polebased approximation of the Fermidirac function
Lin, L; Lu, J; Ying, L; Weinan, E (Chinese Annals of Mathematics. Series B, 20091201)Two approaches for the efficient rational approximation of the FermiDirac function are discussed: one uses the contour integral representation and conformal mapping, and the other is based on a version of the multipole ... 
Quantitative canvas weave analysis using 2D synchrosqueezed transforms: Application of timefrequency analysis to art investigation
Brown, WP; Daubechies, Ingrid; Lu, Jianfeng; Yang, Haizhao; Ying, L (IEEE Signal Processing Magazine, 20150701)© 19912012 IEEE.Quantitative canvas weave analysis has many applications in art investigations of paintings, including dating, forensics, and canvas rollmate identification [1]?[3]. Traditionally, canvas analysis is based ... 
Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms: Application of timefrequency analysis to art investigation
Yang, H; Lu, J; Brown, WP; Daubechies, I; Ying, L (Signal Processing Magazine, IEEE, 201507)Quantitative canvas weave analysis has many applications in art investigations of paintings, including dating, forensics, and canvas rollmate identification. Traditionally, canvas analysis is based on Xradiographs. Prior ... 
Solving parametric PDE problems with artificial neural networks
Khoo, Y; Lu, J; Ying, L (20171130)The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often ... 
Sparsifying preconditioner for soliton calculations
Lu, J; Ying, L (Journal of Computational Physics, 20160615)© 2016 Elsevier Inc.We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative ... 
Synchrosqueezed curvelet transform for twodimensional mode decomposition
Yang, H; Ying, L (SIAM Journal on Mathematical Analysis, 20140101)© 2014 Society for Industrial and Applied Mathematics.This paper introduces the synchrosqueezed curvelet transform as an optimal tool for twodimensional mode decomposition of wavefronts or banded wavelike components. The ... 
Synchrosqueezed wave packet transform for 2D mode decomposition
Yang, H; Ying, L (SIAM Journal on Imaging Sciences, 20131022)This paper introduces the synchrosqueezed wave packet transform as a method for analyzing twodimensional images. This transform is a combination of wave packet transforms of a certain geometric scaling, a reallocation technique ...