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Extremal Point Methods

  • Edward B. Saff
  • Vilmos Totik
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 316)

Abstract

The fact that the weighted equilibrium potential simultaneously solves a certain Dirichlet problem on connected components of C\S w coupled with the fact that the Fekete points are distributed according to the equilibrium distribution leads to a numerical method for determining Dirichlet solutions. However, the determination of the Fekete points is a hard problem, so first we consider an associated sequence a n that is adaptively generated from earlier points according to the law: a n is a point where the weighted polynomial expression
$$ |\left( {z - {{a}_{0}}} \right)\left( {z - {{a}_{1}}} \right) \cdots \left( {z - {{a}_{{n - 1}}}} \right)\omega {{\left( z \right)}^{n}}| $$
takes its maximum on . These so-called Leja points are again distributed like the equilibrium distribution, so we can use them in place of weighted Fekete points.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Edward B. Saff
    • 1
  • Vilmos Totik
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of South Florida Institute for Constructive MathematicsTampaUSA
  2. 2.Bolyai InstituteJozsef Attila UniversitySzegedHungary
  3. 3.Department of MathematicsUniversity of South FloridaTampaUSA

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