On the quality of complementary bounds for eigenvalues

Lyonell Boulton, Aatef Hobiny

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
JournalCalcolo
Volume52
Issue number4
DOIs
Publication statusPublished - Dec 2015

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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