Malaysian Journal of Mathematical Sciences, May 2015, Vol. 9, No. 2
On the Convergence of the Point Repeated Symmetric Single-Step Procedure for Simultaneous Estimation of Polynomial Zeros
Mansor Monsi, Syaida Fadhilah Muhamad Rusli, Nasruddin Hassan, Fudziah Ismail and Zarina Bibi Ibrahim
Corresponding Email: nas@ukm.edu.my
Received date: -
Accepted date: -
Abstract:
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 $(2r+1) (r \geq 1)$. 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.
Keywords: Point procedure, $R$-order of convergence, simple zeros, simultaneous estimation
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