Explicit Error Estimates for Eigenvalues of Some Unbounded Jacobi Matrices

Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)

Abstract

We consider the self-adjoint operator J defined by an infinite Jacobi matrix in the case when the diagonal entries (dk)∞1 form an increasing sequence dk ∞ and the off-diagonal entries (bk)∞1 are small with respect to (dk+1dk)∞1.The main result of this paper is an explicit estimate of the difference between the nth eigenvalue of J and the corresponding eigenvalue of a finite-dimensional block of the original Jacobi matrix.

Keywords

Jacobi matrices eigenvalue estimates error estimates Rayleigh–Ritz method. 

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© Springer Basel 2012

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Paris Diderot Paris 7ParisFrance
  2. 2.LMPA, Centre Universitaire de la Mi-VoixUniversité du LittoralCalais CedexFrance

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