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QR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approach

  • Steven Delvaux
  • Luca Gemignani
  • Marc Van Barel
Part of the Operator Theory: Advances and Applications book series (OT, volume 199)

Abstract

A general scheme is proposed for computing the QR-factorization of certain displacement structured matrices, including Cauchy-like, Vandermonde- like, Toeplitz-like and Hankel-like matrices, hereby extending some earlier work for the QR-factorization of the Cauchy matrix. The algorithm employs a chasing scheme for the recursive construction of a diagonal plus semiseparable matrix of semiseparability rank r, where r is equal to the given displacement rank. The complexity is O(r 2 n 2 ) operations in the general case, and O(rn 2 ) operations in the Toeplitz- and Hankel-like case, where n denotes the matrix size. Numerical experiments are provided.

Mathematics Subject Classification (2000)

65F18 15A23 15A03 

Keywords

Displacement structures QR-factorization lower semiseparable plus diagonal matrices chasing procedure 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Steven Delvaux
    • 1
  • Luca Gemignani
    • 2
  • Marc Van Barel
    • 3
  1. 1.Department of Computer ScienceKatholieke Universiteit LeuvenLeuven (Heverlee)Belgium
  2. 2.Department of MathematicsKatholieke Universiteit LeuvenLeuven (Heverlee)Belgium
  3. 3.Dipartimento di MatematicaUniversità di PisaPisaItaly

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