Error Estimates for the Carathéodory-Fejér Method in Polynomial Approximation

  • Manfred Hollenhorst
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)


In the Carathéodory-Fejér method one computes — starting from a complex power series absolutely convergent on the unit disk — a polynomial which is (hopefully) a better approximation to the function given by the power series than the truncated power series (with respect to the supremum norm). In this article we show that — under fairly restrictive conditions on the coefficients of the power series — the Carathéodory-Fejér method gives an asymptotically optimal approximation and in some cases is really a better approximation than the truncated power series.


Power Series Polynomial Approximation Blaschke Product Supremum Norm Complex Coefficient 
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Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • Manfred Hollenhorst
    • 1
  1. 1.Computer CenterJustus Liebig UniversityGiessenGermany

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