Error bounds for the Lanczos methods for approximating matrix exponentials

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16 Scopus citations


In this paper, we present new error bounds for the Lanczos method and the shift-andinvert Lanczos method for computing e-τAν for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos method will converge rapidly if the matrix A is well-conditioned, regardless of what the norm of τ A is. Numerical examples are given to demonstrate the theoretical bounds.

Original languageEnglish
Pages (from-to)68-87
Number of pages20
JournalSIAM Journal on Numerical Analysis
Issue number1
StatePublished - 2013


  • Krylov subspace method
  • Lanczos method
  • Matrix exponential

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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