Best Approximation of Polynomials on the Sphere and on the Ball

  • Nikolay N. Andreev
  • Vladimir A. Yudin
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 137)


In this paper an approach for finding polynomials of minimum deviation from zero on the sphere and on the ball of n—dimensional Euclidean space is described.


Steklov Institute Minimum Deviation Chebyshev Polynomial Dimensional Euclidean Space 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.


  1. [1]
    N. N. Andreev, V. A. Yudin: Polynomials of minimum deviation from zero and cubature formulas of Chebyshev type, Proceedings Steklov Inst., to appear (2001).Google Scholar
  2. [2]
    H. Ehlich, K. Zeller: Čebyšev-Polynome in mehreren Veränderlichen, Math. Z. 93 (1966), 142–143.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    W. B. Gearhart: Some Chebyshev approximations by polynomials of two variables, J. Approx. Theory 8 (1973), 195–209.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    M. Reimer: Constructive theory of multivariate functions with an application to tomography, Wissenschaftsverlag, MannheimWien-Ziirich 1990.MATHGoogle Scholar
  5. [5]
    M. Reimer: Spherical polynomial approximations. A Survey, Advances in Multivariate Approximation, Math. Research 107, W. Haußmann, K. Jetter, M. Reimer (eds.), Wiley-VCH, Berlin 1999, pp. 231–252.Google Scholar
  6. [6]
    J. M. Sloss: Chebyshev approximation to zero, Pacific J. Math. 15 (1965), 305–313.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Nikolay N. Andreev
    • 1
  • Vladimir A. Yudin
    • 2
  1. 1.Department of Function TheorySteklov Institute of MathematicsMoscowRussia
  2. 2.Department of Higher MathematicsMoscow Institute of Power EngineeringMoscowRussia

Personalised recommendations