Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bernhard Beckermann. The condition number of real Vandermonde, Krylov and positive definite Hankel matrices. Numer. Math., 85(4):553–577, 2000.
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.
Åke Björck and Victor Pereyra. Solution of Vandermonde systems of equations. Math. Comp., 24(112):893–903, 1970.
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.
Nicholas J. Higham. Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Numer. Math., 50(5):613–632, 1987.
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.
J. F. Traub. Associated polynomials and uniform methods for the solution of linear problems. SIAM Rev., 8(3):277–301, 1966.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Higham, N.J. (2014). Numerical conditioning. In: Brezinski, C., Sameh, A. (eds) Walter Gautschi, Volume 1. Contemporary Mathematicians. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7034-2_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7034-2_5
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4614-7033-5
Online ISBN: 978-1-4614-7034-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)