Decay estimates of discretized Green’s functions for Schrödinger type operators


Journal Article

© 2016, Science China Press and Springer-Verlag Berlin Heidelberg. 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.

Full Text

Duke Authors

Cited Authors

  • Lin, L; Lu, J

Published Date

  • August 1, 2016

Published In

Volume / Issue

  • 59 / 8

Start / End Page

  • 1561 - 1578

International Standard Serial Number (ISSN)

  • 1674-7283

Digital Object Identifier (DOI)

  • 10.1007/s11425-016-0311-4

Citation Source

  • Scopus