Numerical conditioning

  • Nicholas J. Higham
Part of the Contemporary Mathematicians book series (CM)


A theme running through Gautschi’s work is numerical conditioning. His many papers on this topic fall broadly into two categories: those on conditioning of Vandermonde matrices and those on conditioning of polynomials.


  1. 1.
    Bernhard Beckermann. The condition number of real Vandermonde, Krylov and positive definite Hankel matrices. Numer. Math., 85(4):553–577, 2000.Google Scholar
  2. 2.
    T. Bella, Y. Eidelman, I. Gohberg, I. Koltracht, and V. Olshevsky. A fast Björck–Pereyra-type algorithm for solving Hessenberg-quasiseparable-Vandermonde systems. SIAM J. Matrix Anal. Appl., 31(2):790–815, 2009.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Åke Björck and Victor Pereyra. Solution of Vandermonde systems of equations. Math. Comp., 24(112):893–903, 1970.Google Scholar
  4. 4.
    James W. Demmel and Plamen Koev. The accurate and efficient solution of a totally positive generalized Vandermonde linear system. SIAM J. Matrix Anal. Appl., 27(1): 142–152, 2005.Google Scholar
  5. 5.
    Nicholas J. Higham. Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Numer. Math., 50(5):613–632, 1987.Google Scholar
  6. 6.
    Nicholas J. Higham. Accuracy and stability of numerical algorithms. Second edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. xxx+680 pp. ISBN 0-89871-521-0.Google Scholar
  7. 7.
    J. F. Traub. Associated polynomials and uniform methods for the solution of linear problems. SIAM Rev., 8(3):277–301, 1966.MathSciNetCrossRefMATHGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Nicholas J. Higham
    • 1
  1. 1.School of MathematicsThe University of ManchesterManchesterUK

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