Remarks on "On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency"

An oversight on the number of function evaluations of the $n$-point root-finding methods proposed in [SIAM J. Numer. Anal., 47 (2010), pp. 4402-4414] is discussed. To correct this flaw, modified methods of optimal computational efficiency are presented by applying higher-order Hermite interpolatory polynomials.