On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis

  • Tom Lyche
  • Karl Scherer
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 125)


We give an upper bound for the L condition number of the triangular Bernstein basis for polynomials of total degree at most n in s variables. The upper bound grows like (s + 1) n when n tends to infinity. Moreover the upper bound is independent of s for sn — 1.


Condition Number Asymptotic Formula Total Degree Bernstein Basis Chebyshev System 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Tom Lyche
    • 1
  • Karl Scherer
    • 2
  1. 1.Institutt for informatikkUniversity of OsloBlindemOsloNorway
  2. 2.Institut für angewandte MathematikRheinische Friedrich-Wilhems-Universität BonnBonnGermany

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