Publications [#318294] of Jianfeng Lu

Papers Published

1. Lin, L; Lu, J, Decay estimates of discretized Green’s functions for Schrödinger type operators, Science China Mathematics, vol. 59 no. 8 (August, 2016), pp. 1561-1578, Springer Nature [doi]
   (last updated on 2026/01/16)

   Abstract:
   For a sparse non-singular matrix A, generally A⁻¹ is a dense matrix. However, for a class of matrices, A⁻¹ can be a matrix with off-diagonal decay properties, i.e., |Aij ⁻¹| decays fast to 0 with respect to the increase of a properly defined distance between i and j. Here we consider the off-diagonal decay properties of discretized Green’s functions for Schrödinger type operators. We provide decay estimates for discretized Green’s functions obtained from the finite difference discretization, and from a variant of the pseudo-spectral discretization. The asymptotic decay rate in our estimate is independent of the domain size and of the discretization parameter. We verify the decay estimate with numerical results for one-dimensional Schrödinger type operators.