On the convergence of the point repeated symmetric single-step procedure for simultaneous estimation of polynomial zeros - Monsi, Mansor; Muhamad Rusli, Syaida Fadhilah; Hassan, Nasruddin; Ismail, Fudziah; Bibi, Zarina (Institute for Mathematical Research, Universiti Putra Malaysia, 2015)
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.