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Convergence of the Arnoldi Process when applied to the Picard-Lindelöf Iteration Operator

by S. Hyvönen

(Report number 1996-03)

Abstract
In this paper the iteration operator corresponding to the Picard-Lindelöf iteration is considered as a model case in order to investigate the convergence theory of the Arnoldi process. We ask whether it is possible to use a theorem by Nevanlinna and Vainikko to obtain the spectrum of the local operator. In the cases considered here the answer is no.

Keywords: Arnoldi method, Picard-Lindelöf iteration

@Techreport{H96_186,
  author = {S. Hyv\"onen},
  title = {Convergence of the Arnoldi Process when applied to the Picard-Lindel\"of Iteration Operator},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-03.pdf },
  year = {1996}
}

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