The Ratio Between the Toeplitz and the Unstructured Condition Number

  • Siegfried M. Rump
  • Hiroshi Sekigawa
Part of the Operator Theory: Advances and Applications book series (OT, volume 199)


Recently it was shown that the ratio between the normwise Toeplitz structured condition number of a linear system and the general unstructured condition number has a finite lower bound. However, the bound was not explicit, and nothing was known about the quality of the bound. In this note we derive an explicit lower bound only depending on the dimension n, and we show that this bound is almost sharp for all n.

Mathematics Subject Classification (2000)

15A12 26D05 


Structured condition number Toeplitz matrix Mahler measure polynomial norms 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Siegfried M. Rump
    • 1
    • 2
  • Hiroshi Sekigawa
    • 3
  1. 1.Institute for Reliable ComputingHamburg University of TechonologyHamburgGermany
  2. 2.Faculty of Science and EngineeringWaseda UniversityTokyoJapan
  3. 3.NTT Communication Science LaboratoriesNippon Telegraph and Telephone CorporationKanagawaJapan

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