On the convergence of the point repeated symmetric single-step procedure for simultaneous estimation of polynomial zeros

The point symmetric single-step procedure established by monsi (2012) has r-order of convergence at least 3. this procedure is modified by repeating the steps in the procedure r times without involving function evaluations. this modified procedure is called the point repeated symmetric single-step prss1. the r-order of convergence of prss1 is at least (2r + 1) (r=1). computational experiences in the implementation of the interval version of prss1 (see monsi and wolfe,1988) showed that the repeated symmetric single-step procedure is more efficient than the total step (kerner,1966) and the single-step (alefeld and herzberger,1974) methods.