Basins of attraction for family of Popovski’s methods and their extension to multiple roots

Beny Neta

doi:10.33993/jnaat511-1248

Authors

Beny Neta Naval Postgraduate School, Monterey, USA

DOI:

https://doi.org/10.33993/jnaat511-1248

Keywords:

Nonlinear equations, simple roots, multiple roots, basins of attraction, Popovski's method

Abstract views: 235

Abstract

In this paper we revisit Popovski’s family of methods for simple roots. We compare several members using basins of attraction visually and qualitatively by comparing the run-time on several examples, the average number of iterations and the number of divergent points. We chose 5 different members of the family. We also develop an equivalent family of methods for multiple roots and compare several members on six different numerical examples.

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