ABSTRACT
This chapter is concerned with the problem of approximating a locally unique solution of a nonlinear equation. The convergence matter is usually divided in local and semilocal study. The local study is based on the solution whereas the semilocal one is based on the initial point. The chapter provides a semilocal convergence analysis for Halley’s method. It discusses the most used conditions for the study of the semilocal convergence of Halley’s method, with numerical examples. The chapter also presents some basins of attraction related to Halley’s method applied to different polynomials with different roots with different multiplicities.
