BIT Numerical Mathematics

, Volume 33, Issue 1, pp 74–84 | Cite as

The stability of rational approximations of analytic semigroups

  • M. Crouzeix
  • S. Larsson
  • S. Piskarev
  • V. Thomée
Part II Numerical Mathematics


It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.

1980 Mathematics Subject Classification (1985 Revision)

65J10 65M12 

Key words and phrases

Analytic semigroup Banach space rational approximation A-acceptable A(θ)-acceptable stability  Crank-Nicolson method 


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Copyright information

© BIT Foundations 1993

Authors and Affiliations

  • M. Crouzeix
    • 1
  • S. Larsson
    • 2
  • S. Piskarev
    • 2
  • V. Thomée
    • 2
  1. 1.Institut Mathématique et IRISAUniversité de Rennes IRennes CedexFrance
  2. 2.Department of MathematicsChalmers University of TechnologyGöteborgSweden

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