4 papers
An optimal complexity spectral solver for the Poisson equation
Ouyuan Qin
We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction impl…
A new banded Petrov--Galerkin spectral method
Ouyuan Qin, Lu Cheng, Kuan Xu
We propose a Petrov--Galerkin spectral method for ODEs with variable coefficients. When the variable coefficients are smooth, the new method yields a strictly banded linear system,…
Computing the -Laplacian eigenpairs of signed graphs
Chuanyuan Ge, Ouyuan Qin
As a nonlinear extension of the graph Laplacian, the graph -Laplacian has various applications in many fields. Due to the nonlinearity, it is very difficult to compute the eigen…
Solving nonlinear ODEs with the ultraspherical spectral method
Ouyuan Qin, Kuan Xu
We extend the ultraspherical spectral method to solving nonlinear ODE boundary value problems. We propose to use the inexact Newton-GMRES framework for which an effective precondit…