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International Conference on Numerical Analysis and Its Applications

NAA 2000: Numerical Analysis and Its Applications pp 51–58Cite as

Stability Analysis of Parallel Evaluation of Finite Series of Orthogonal Polynomials

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Abstract

In this paper we study the rounding errors in the parallel evaluation of a finite series of a general family of orthogonal polynomials. Both, the theoretical bounds and the numerical tests present an almost similar behavior between the sequential and the parallel algorithms.

The first author is supported partially by the Spanish Ministry of Education and Science (Project #ESP99-1074-CO2-01) and by the Centre National d’Études Spatiales at Toulouse (France). The second author is supported partially by Grants MM-707/97 and I-702/97 from the Bulgarian Ministry of Education and Science.

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References

  1. Barrio, R.: Parallel algorithms to evaluate orthogonal polynomial series, to appear on SIAM J. Sci. Comput.

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  2. Barrio, R.: Stability of parallel algorithms to evaluate Chebyshev series, submitted to Comput. Math. Appl.

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  3. Barrio, R. and Sabadell, J.: Parallel evaluation of Chebyshev and Trigonometric series, Comput. Math. Appl., 38 (1999), 99–106.

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  4. Barrio, R. and Yalamov, P. Y.: Stability of parallel algorithms for polynomial evaluation, submitted to SIAM J. Sci. Comput.

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  5. Higham, N. J.: Accuracy and stability of numerical algorithms, SIAM, Philadelphia, (1996).

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Author information

Authors and Affiliations

  1. GME, Depto. Matemática Aplicada, Edificio de Matemáticas University of Zaragoza, E-50009, Zaragoza, Spain

    Roberto Barrio

  2. Center of Applied Mathematics and Informatics University of Rousse, 7017, Rousse, Bulgaria

    Plamen Yalamov

Authors
  1. Roberto Barrio
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  2. Plamen Yalamov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Barrio, R., Yalamov, P. (2001). Stability Analysis of Parallel Evaluation of Finite Series of Orthogonal Polynomials. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_7

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  • DOI: https://doi.org/10.1007/3-540-45262-1_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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