An analogue of the results of Saad and Stewart for harmonic Ritz vectors

  • Authors:

  • Guizhi Chen;Zhongxiao Jia

  • Affiliations:

  • Department of Mathematics, Xiamen University, Xiamen 361005, PR China;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2004

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Abstract

Let (λ,x) be an eigenpair of the matrix A of order n and let (µ,u) be a Ritz pair of A with respect to a subspace K. Saad has derived a simple priori error bound for sin ∠(x, u) in terms of sin ∠(x, K) for A Hermitian. Similar to Saad's result, Stewart has got an equally simple inequality for A non-Hermitian. In this paper, let (θ, w) be a harmonic Ritz pair from a subspace K, a similar priori error bound for sin ∠(x, w) is established in terms of sin ∠(x, K).