Journal of Mathematical Sciences

, Volume 90, Issue 5, pp 2416–2420 | Cite as

Padé approximation and generalized moments

  • M. M. Chip


We propose studying generalized moment representations of a form in which it suffices to apply a system of orthogonal polynomials in order to procure the biorthogonality conditions in the construction of superdiagonal Padé polynomials using generalized moment representations. The algebraic polynomials in the moment representation are to be sought as the linear forms of biorthogonal polynomials. We obtain the relations between the coefficients of these linear forms and the generalized moments, and we also establish conditions for the existence and uniqueness of generalized moment representations of polynomial form.


Linear Form Orthogonal Polynomial Linear Algebraic Equation Polynomial Form Algebraic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    G. Baker and P. R. Graves-Morris,Padé Approximants, Addison-Wesley, Reading, MA (1981).Google Scholar
  2. 2.
    F. R. Gantmakher,Theory of Matrices, nelsea, New York (1959)Google Scholar
  3. 3.
    W. Jones and W. Thron,Continued Fractions, Addison-Wesley, Reading, MA (1980).Google Scholar
  4. 4.
    V. K. Dzyadyk, “The generalized moment problem and Padé approximation,”Ukr. Mat. Zh.,35, No. 3, 297–302 (1983).MATHMathSciNetGoogle Scholar
  5. 5.
    V. K. Dzyadyk and A. P. Golub, “The generalized moment problem and Padé approximation,” Preprint, Mathematical Institute of the Academy of Sciences of the Ukrainian SSR, Kiev (1981), pp. 58–81.Google Scholar
  6. 6.
    M. M. Chip, “Methods of constructing generalized moment representations of polynomial form,”Ukr. Mat. Zh.,44, No. 7, 995–997 (1992).MATHMathSciNetGoogle Scholar
  7. 7.
    J. Gilewicz,Approximants de Padé, Lect. Notes Math.,667, Springer, New York (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • M. M. Chip

There are no affiliations available

Personalised recommendations