On the convergence rate of symmetric single-step method ISS for simultaneous bounding polynomial zeros (Q2898633)

This manuscript is written very coarsely and inaccurately, not only in mathematical description but also in English writing, almost all the theorems and the numerical schemes are directly taken from the existing literature, and the latest literature to be cited by the manuscript is back to 1999, and others are back to 1970s and 1980s, obviously the topic to be studied is a very old one. The reviewer finds that the only contribution of this manuscript may be Theorem 2.1 and its proof, even then, the improvement of this theorem over the original Theorem 1.1 lacks a substantial contribution very much, likewise does its proof.NEWLINENEWLINESome obvious improper things are that the function \(w\) has been never defined but apparently it is an important tool used everywhere in the proof; and the numerical results are not explained clearly, especially the most important convergence rate is not demonstrated by using neither the data nor the theorem.