On the quality of complementary bounds for eigenvalues

Lyonell Boulton*, Aatef Hobiny

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


A concrete formulation of the Lehmann–Maehly–Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determined in terms of how well the trial spaces capture the spectral subspace of the operator. Optimality of the choice of a shift parameter which is intrinsic to the method is also examined. The main theoretical findings are illustrated by means of a few numerical experiments involving one-dimensional Schrödinger operators.

Original languageEnglish
Pages (from-to)577-601
Number of pages25
Issue number4
Publication statusPublished - Dec 2015


  • Complementary eigenvalue bounds
  • Eigenvalue computation
  • Lehmann–Maehly–Goerisch method
  • Zimerman–Mertins method

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


Dive into the research topics of 'On the quality of complementary bounds for eigenvalues'. Together they form a unique fingerprint.

Cite this