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A duality view of spectral methods for dimensionality reduction
Duality spectrum the nonlinear dimension reduction locally linear embedding Laplacian sparse matrix
2015/8/10
We present a unified duality view of several recently emerged spectral methods for nonlinear dimensionality reduction, including Isomap, locally linear embedding, Laplacian eigenmaps, and maximum vari...
Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the Wright-Fisher model
Bivariate Markov processes switching di usions matrix-valued orthogonal functions Wright-Fisher models
2011/9/14
Abstract: The aim of this paper is to study differential and spectral properties of the infinitesimal operator of two dimensional Markov processes with diffusion and discrete components. The infinites...
Non-equilibrium allele frequency spectra via spectral methods
Non-equilibrium allele frequency spectra spectral methods
2010/11/24
A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amou...
Spectral Methods in PDE
Spectral Methods PDE
2010/11/30
This is to review some recent progress in PDE. The emphasis is on (energy)supercritical nonlinear Schr¨odinger equations. The methods are applicable to other nonlinear equations.
CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM
Least-squares methods Spectral method Negative norm
2007/12/12
We develop and analyze a first-order system least-squares spectral
method for the second-order elliptic boundary value problem with
variable coefficients. We first analyze the Chebyshev weighted nor...
A New Parallel Strategy for Two-dimensional Incompressible Flow Simulations Using Pseudo-spectral Methods
Parallel computing Pseudo-spectral methods Task distribution Navier-Stokes equations Boussinesq equations
2012/7/31
A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It ta...
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit
Spectral methods Boltzmann equation cut-off assumption Fokker-Planck-Landau equation
2010/12/14
In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the socalled grazing collision limit.