Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method

摘要

There are relatively few optimal fourth order methods for solving nonlinear algebraic equations having roots of known multiplicity m. In a previous paper we have compared 5 such methods, two of which require the evaluation of the (m−1)st root. We have used the basin of attraction idea to recommend the best optimal fourth order method. Here we compare the family of methods developed by Kanwar et al. (2013)– to the best known method. We will also point out some mistake in deriving that family.