Abstract
A rational interpolation is obtained by solving a system of linear equations. However, when the system is solved by floating point arithmetic, there appears a pathological feature such as undesired zeros and poles. In this paper, a method is described with the help from computer assisted proof to eliminate the feature.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
B. Beckermann, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math., 85, pp. 553–577, 2000.
J. W. Demmel, On condition numbers and the distance to the nearest ill-posed problem, Numer. Math., 51, pp. 251–289, 1995.
H. Kai and M.-T. Noda, Hybrid rational function approximation and its accuracy analysis, Reliable Computing, 6, pp. 429–438, 2000.
Y. Murakami, H. Kai and M.-T. Noda, Approximate algebraic computation for rational function approximations, ACA’ 2002, http://www.hpc.cs.ehime-u.ac.jp/~aca2002/abstract/murakami.pdf, 2002.
Y. Murakami, H. Kai and M.-T. Noda, Hybrid rational function approximation and ill-conditioned property, J. JSSAC, 11(3,4), pp. 141–152, 2005 (in Japanese).
M.-T. Noda, E. Miyahiro and H. Kai, Hybrid rational function approximation and its use in the hybrid integration, Advances in Computer Methods for Partial Differential Equations VII, edited by R. Vichnevetsky, D. Knight and G. Richter, pp. 565–571, IMACS, 1992.
S. Oishi and S. M. Rump, Fast verification of solutions of matrix equations, Numer. Math., 90, pp. 755–773, 2002.
R. Kacheong Yeung, Stable Rational Interpolation, Ph.D, Computing Science, University of Alberta, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Kai, H. (2007). Rational Interpolation and Its Ill-conditioned Property. In: Wang, D., Zhi, L. (eds) Symbolic-Numeric Computation. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7984-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7984-1_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7983-4
Online ISBN: 978-3-7643-7984-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)