The strength of nonstationary iteration

G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This is the second of three papers in which we study global convergence of iterations using linear information for the solution of nonlinear equations. In Wasilkowski [6] we proved that for the class of all analytic scalar complex functions having only simple zeros there exists no globally convergent stationary iteration using linear information. Here we exhibit a nonstationary iteration using linear information which is globally convergent even for the multivariate and abstract cases. This demonstrates the strength of nonstationary iteration. In Wasilkowski [7] we shall prove that any globally convergent iteration using linear information has infinite complexity even for the class of scalar complex polynomials having only simple zeros.

Original languageEnglish
Pages (from-to)243-260
Number of pages18
JournalAequationes Mathematicae
Issue number1
StatePublished - Dec 1982


  • AMS (1980) subject classification: Primary 65H10

ASJC Scopus subject areas

  • Mathematics (all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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