10 citations · 19 across the 21 of their papers we have counts for
4 papers · 1 filter
Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to Schrödinger Operators
Xuefeng Liu
Spectral Galerkin methods are renowned for high-precision eigenvalue approximation, yet a rigorous lower bound obtained directly from a spectral discretisation has remained unavail…
Explicit Two-Sided Eigenvalue Bounds for Schrödinger Operators with Singular Potentials via Finite Element Method
Xuefeng Liu
We present, to the best of our knowledge, the first numerical algorithm for explicit, computable two-sided eigenvalue bounds for Schrödinger operators H = -Delta + V on R^N, N = 2,…
Sharp Dirichlet eigenvalue inequalities on triangles
Ryoki Endo, Xuefeng Liu, Phanuel Mariano
We prove sharp Dirichlet eigenvalue inequalities for planar triangles. We settle a conjecture of Laugesen and Siudeja by showing that the equilateral triangle uniquely minimizes a…
Rigorous Eigenvalue Bounds for Schrödinger Operators with Confining Potentials on
Xuefeng Liu
We propose a rigorous method for computing two-sided eigenvalue bounds of the Schrödinger operator with a confining potential on . The method combines domain…