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Epsilon-algorithm and eta-algorithm of generalized inverse function-valued padé approximants using for solution of integral equations

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Abstract

Two efficient recursive algorithms epsilon-algorithm and eta-algorithm are introduced to compute the generalized inverse function-valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function-valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Padé approximants is also established by means of the connection of two algorithms.

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References

  1. Chisholm J S R. Solution of integral equations using Padé approximants[J].J Math Phys, 1963,4, (12):1506–1510.

    Article  MATH  MathSciNet  Google Scholar 

  2. Graves-Morris P R. Solution of integral equations using generalized inverse, function-valued Padé approximants[J].J Comput Appl Math, 1990,32(1):117–124.

    Article  MATH  MathSciNet  Google Scholar 

  3. Coope I D, Graves-Morris P R. The rise and fall of the vector epsilon algorithm[J].Numerical Algorithms, 1993,5(2):275–286.

    Article  MATH  MathSciNet  Google Scholar 

  4. GU Chuan-qing, LI Chun-jing. Computation formulas of generalized inverse Padé approximant using for solution of integral equation[J].Applied Mathematics and Mechanics (English Edition), 2001,22(9):1057–1063.

    MathSciNet  Google Scholar 

  5. Baker G A.The Numerical Treatment of Integral Equations[M]. London: Oxford Univ Press, 1978.

    Google Scholar 

  6. GU Chuan-qing. Generalized inverse matrix Padé approximation on the basis of scalar product[J].Linear Algebra Appl, 2001,322(1–3):141–167.

    MathSciNet  Google Scholar 

  7. Baker G A, Graves-Morris P R.Padé Approximants (Part I) [M]. Massachusetts: Addison-Wesley Publishing Company, 1981.

    Google Scholar 

  8. Graves-Morris P R, Jenkins C D. Vector valued rational interpolants III[J].Constr Approx, 1986,2(2):263–289.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, 200436, Shanghai, P.R. China

    Li Chun-jing Doctor & Gu Chuan-qing Professor

  2. Department of Mathematics, Tongji University, 200331, Shanghai, P.R. China

    Li Chun-jing Doctor

Authors
  1. Li Chun-jing Doctor
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  2. Gu Chuan-qing Professor
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Additional information

Communicated by LIU Yu-lu

Foundation items: the National Natural Science Foundation of China (10271074)

Biographies: LI Chun-jing (1958 −) GU Chuan-qing (1955 −)

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Chun-jing, L., Chuan-qing, G. Epsilon-algorithm and eta-algorithm of generalized inverse function-valued padé approximants using for solution of integral equations. Appl Math Mech 24, 221–229 (2003). https://doi.org/10.1007/BF02437629

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  • DOI: https://doi.org/10.1007/BF02437629

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