3 papers
math.NA2025
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…
math.NA2025
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,…
math.NA2025
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…