3 papers
math.SP2025
Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered Eigenvalues
Ryoki Endo, Xuefeng Liu
The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape differenc…
math.SP2025
The second Dirichlet eigenvalue is simple on every non-equilateral triangle
Ryoki Endo, Xuefeng Liu
The Dirichlet eigenvalues of the Laplacian on a triangle that collapses into a line segment diverge to infinity. In this paper, to track the behavior of the eigenvalues during the…
math.NA2021
Error constant estimation under the maximum norm for linear Lagrange interpolation
Shirley Mae Galindo, Koichiro Ike, Xuefeng Liu
For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using t…