Linear Convergence

  • Olavi Nevanlinna
Part of the Lectures in Mathematics ETH Zürich book series (LM)

Abstract

The iteration
$$x^k:=Lx^{k-1}+g$$
(3.1.1)
converges linearly with the speed determined by the spectral radius ρ(L) (when ρ (L) < 1 and the initial guess is “generic”). In particular this speed is completely determined by the spectrum; the growth of the resolvent near the spectrum only shows up in the time it takes to settle down to this speed.

Keywords

Chebyshev Polynomial Subharmonic Function Optimal Polynomial Unbounded Component Polynomial Sequence 
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.

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Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  • Olavi Nevanlinna
    • 1
  1. 1.Institute of MathematicsHelsinki University of TechnologyEspooFinland

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