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Rational Interpolation and Its Ill-conditioned Property

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Book cover Symbolic-Numeric Computation

Part of the book series: Trends in Mathematics ((TM))

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.

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References

  1. B. Beckermann, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math., 85, pp. 553–577, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. W. Demmel, On condition numbers and the distance to the nearest ill-posed problem, Numer. Math., 51, pp. 251–289, 1995.

    Article  MathSciNet  Google Scholar 

  3. H. Kai and M.-T. Noda, Hybrid rational function approximation and its accuracy analysis, Reliable Computing, 6, pp. 429–438, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  4. 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.

    Google Scholar 

  5. 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).

    Google Scholar 

  6. 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.

    Google Scholar 

  7. S. Oishi and S. M. Rump, Fast verification of solutions of matrix equations, Numer. Math., 90, pp. 755–773, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Kacheong Yeung, Stable Rational Interpolation, Ph.D, Computing Science, University of Alberta, 1999.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8977, Japan

    Hiroshi Kai

Authors
  1. Hiroshi Kai
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Editor information

Editors and Affiliations

  1. School of Science, Beihang University, 37 Xueyuan Road, Beijing, 100083, China

    Dongming Wang

  2. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie - CNRS, 8, rue due Capitaine Scott, 75015, Paris, France

    Dongming Wang

  3. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Beijing, 100080, China

    Lihong Zhi

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© 2007 Birkhäuser Verlag Basel/Switzerland

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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

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