4 citations · 13 across the 13 of their papers we have counts for
13 papers
A FEAST variant incorporated with a power iteration
Man-Chung Yeung, Long Lee
We present a variant of the FEAST matrix eigensolver for solving restricted real and symmetric eigenvalue problems. The method is derived from a combination of a variant of the FEA…
Numerical renormalization group algorithms for self-similar solutions of partial differential equations
Gastão A. Braga, Federico C. Furtado, Vincenzo Isaia +1
We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on…
A Spectral Projection Preconditioner for Solving Ill Conditioned Linear Systems
Man-Chung Yeung, Craig C. Douglas, Long Lee
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our result…
On Solving Ill-Conditioned Linear Systems
Craig C. Douglas, Long Lee, Man-Chung Yeung
This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our…
A landmark-based algorithm for automatic pattern recognition and abnormality detection
S. Huzurbazar, Long Lee, Dongyang Kuang
We study a class of mathematical and statistical algorithms with the aim of establishing a computer-based framework for fast and reliable automatic abnormality detection on landmar…
A class of fast geodesic shooting algorithms for template matching and its applications via the -particle system of the Euler-Poincaré equations
Roberto Camassa, Dongyang Kuang, Long Lee
The Euler-Poincaré (EP) equations describe the geodesic motion on the diffeomorphism group. For template matching (template deformation), the Euler-Lagrangian equation, arising fro…
Analysis and development of compact finite difference schemes with optimized numerical dispersion relations
Yi-Hung Kuo, Long Lee, Gregory Lyng
Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential eq…
A connection between the shallow-water equations and the Euler-Poincaré equations
Roberto Camassa, Long Lee
The Euler-Poincaré differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with…
Solitary waves and -particle algorithms for a class of Euler-Poincaré equations
Roberto Camassa, Dongyang Kuang, Long Lee
We study a class of partial differential equations (PDEs) in the family of the so-called Euler-Poincaré differential systems, with the aim of developing a foundation for numerical…
A conservation formulation and a numerical algorithm for the double-gyre nonlinear shallow-water model
Dongyang Kuang, Long Lee
We present a conservation formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to…
The WKB approximation of semiclassical eigenvalues of the Zakharov-Shabat problem
Yeongjoh Kim, Long Lee, Gregory D. Lyng
We numerically compute eigenvalues of the non-self-adjoint Zakharov--Shabat problem in the semiclassical regime. In particular, we compute the eigenvalues for a Gaussian potential…
A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation
Long Lee, Gregory D. Lyng
We present the results of a numerical experiment inspired by the semiclassical (zero-dispersion) limit of the focusing nonlinear Schroedinger (NLS) equation. In particular, we focu…
The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation
Long Lee, Gregory Lyng, Irena Vankova
We report on a number of careful numerical experiments motivated by the semiclassical (zero-dispersion, ε\downarrow 0) limit of the focusing nonlinear Schrödinger equation. Our exp…