Vector Orthogonal Polynomials of Dimension -d

  • C. Brezinski
  • J. Van Iseghem
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)


Vector orthogonal polynomials of dimension -d where d is a nonzero positive integer are defined. They are proved to satisfy a recurrence relation with d + 2 terms. A Shohat-Favard type theorem and a QD like algorithm are given.


Orthogonal polynomials biorthogonality recurrence relations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Brezinski C. Padé-Type Approximation and General Orthogonal Polynomials. ISNM 50, Birkhäuser, Basel, 1980.zbMATHGoogle Scholar
  2. [2]
    Brezinski C. Biorthogonality and its Applications to Numerical Analysis. Marcel Dekker, New York, 1991.Google Scholar
  3. [3]
    Brezinski C. A unified approach to various orthogonalities. Ann. Fac. Sci. Toulouse, ser.3, vol. l, fasc. 3, 277–292, 1992.CrossRefGoogle Scholar
  4. [4]
    Brezinski C. Formal orthogonality on an algebraic curve. Annals of Numer. Math. To appear.Google Scholar
  5. [5]
    Brezinski C., Redivo Zaglia M. Orthogonal polynomials of dimension —1 in the non-definite case. Rend. Mat. Roma, ser. VII, 13, 1993. To appear.Google Scholar
  6. [6]
    Bultheel A. Laurent Series and their Pade Approximations. Birkhauser, Basel, 1987.zbMATHCrossRefGoogle Scholar
  7. [7]
    Draux A. Polynômes Orthogonaux Formels-Applications. LNM 974, Springer Verlag, Berlin, 1987.Google Scholar
  8. [8]
    Van Iseghem J. Vector orthogonal relations. Vector qd-algorithm. J. Comput. Appl. Math., 19: 141–150, 1987.MathSciNetzbMATHGoogle Scholar

Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • C. Brezinski
    • 1
  • J. Van Iseghem
    • 2
  1. 1.Laboratoire d’Analyse Numérique et d’Optimisation, UFR IEEA-M3Université des Sciences et Technologies de LilleVilleneuve d’Ascq cedexFrance
  2. 2.U.F.R. de Mathématiques Pures et AppliquéesUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq cedexFrance

Personalised recommendations