Applied Mathematics and Mechanics

, Volume 24, Issue 2, pp 221–229 | Cite as

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

  • Li Chun-jing
  • Gu Chuan-qing
Article

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.

Key words

generalized inverse function-valued Padé approximant epsilon-algorithm eta-algorithm integral equations 

Chinese Library Classification

O241.83 

2000 MR Subject Classification

41A21 

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References

  1. [1]
    Chisholm J S R. Solution of integral equations using Padé approximants[J].J Math Phys, 1963,4, (12):1506–1510.MATHMathSciNetCrossRefGoogle Scholar
  2. [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.MATHMathSciNetCrossRefGoogle Scholar
  3. [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.MATHMathSciNetCrossRefGoogle Scholar
  4. [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.MathSciNetGoogle Scholar
  5. [5]
    Baker G A.The Numerical Treatment of Integral Equations[M]. London: Oxford Univ Press, 1978.Google Scholar
  6. [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.MathSciNetGoogle Scholar
  7. [7]
    Baker G A, Graves-Morris P R.Padé Approximants (Part I) [M]. Massachusetts: Addison-Wesley Publishing Company, 1981.Google Scholar
  8. [8]
    Graves-Morris P R, Jenkins C D. Vector valued rational interpolants III[J].Constr Approx, 1986,2(2):263–289.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Li Chun-jing
    • 1
    • 2
  • Gu Chuan-qing
    • 1
  1. 1.Department of MathematicsShanghai UniversityShanghaiP.R. China
  2. 2.Department of MathematicsTongji UniversityShanghaiP.R. China

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