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Several root-ratio multipoint methods for finding multiple zeros ofunivariate functions were recently presented. The characteristic of thesemethods is that they deal with $m$-th root of ratio of two functions (hence thename root-ratio methods), where $m$ is the multiplicity of the sought zero,known in advance. Some of these methods were presented without any derivationand motivation, it could be said, out of the blue. In this paper we present aneasy and entirely natural way for constructing root-ratio multipoint iterativemethods starting from multipoint methods for finding simple zeros. In this way,a vast number of root-ratio multipoint methods for multiple zeros, existing aswell new ones, can be constructed. For demonstration, we derive four root-ratiomethods for multiple zeros. Besides, we study computational cost of theconsidered methods and give a comparative analysis that involves CPU timeneeded for the extraction of the $m$-th root. This analysis shows thatroot-ratio methods are pretty inefficient from the computational point of viewand, thus, not suitable in practice. A general discussion on a practical needfor multipoint methods of very high order is also considered.

On root-ratio multipoint methods for finding multiple zeros of univariate functions