Spurious Poles in Diagonal Rational Approximation

  • D. S. Lubinsky
Conference paper
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 19)


Any function f meromorphic in C admits fast rational approximation. That is, if K is a compact set in which f is analytic, there exist rational functions R n of type (n,n),n ≥ 1, such that
$$\mathop {\lim }\limits_{n \to \infty } \left\| {f - {R_n}} \right\|_{{L_\infty }(K)}^{1/n} = 0$$
. More generally, any function f defined on an open set U, and admitting such approximation on a compact KU with positive logarithmic capacity, is said to belong to the Gonchar-Walsh Class on U. We discuss at an introductory, non-technical, level, the problem of spurious poles for diagonal and sectorial sequences of rational approximants to functions in the Gonchar-Walsh class. In particular, we concentrate on some recent positive results on the distribution of poles, and some of their consequences.


Entire Function Rational Approximation Interpolation Point Rational Approximants Interpolation Condition 
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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • D. S. Lubinsky
    • 1
  1. 1.Dept. of MathematicsWitwatersrand UniversityJohannesburgRep. South Africa

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