Newton's method's basins of attraction revisited

H. Susanto, N. Karjanto

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a function of the parameter.

Original languageBritish English
Pages (from-to)1084-1090
Number of pages7
JournalApplied Mathematics and Computation
Volume215
Issue number3
DOIs
StatePublished - 1 Oct 2009

Keywords

  • Iteration methods
  • Newton-Raphson methods
  • Nodules

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