The Point Zoro Symmetric Single‐Step Procedure for Simultaneous Estimation of Polynomial Zeros

Abstract

The point symmetric single step procedure PSS1 hasR-order of convergence at least 3. This procedure is modified by adding another single-step, which is the third step in PSS1. This modified procedure is called the point zoro symmetric single-step PZSS1. It is proven that theR-order of convergence of PZSS1 is at least 4 which is higher than theR-order of convergence of PT1, PS1, and PSS1. Hence, computational time is reduced since this procedure is more efficient for bounding simple zeros simultaneously.

The interval zoro-symmetric single-step procedure IZSS2-5D for the simultaneous bounding of simple polynomial zeros

“…The interval symmetric single-step procedure IZSS2-5D is an extension of the interval single-step procedure ISS2 [11] and interval zoro symmetric single-step procedure IZSS1 [13], based on the idea of [1,2,3,4,7,8,10,12]. The sequence…”

On convergence of the interval zoro symmetric single step procedure for polynomial zeros

“…Iterative procedures for simultaneous inclusion of simple polynomial zeros were discussed by Monsi and Wolfe [1], Jamaludin et al [2][3][4][5][6], Monsi et al [7,8], Sham et al [9][10][11] and Bakar et al [12]. Our interest lies in the procedure proposed by Jamaludin et al [2] as in Section 2, which was shown to be convergent numerically in terms of shorter CPU times and lesser number of iterations using five test polynomials with ( ) 10 10 k w   as the stopping criterion.…”

The Newton’s method in the interval symmetric single step procedure for polynomial zeros

“…Special treatments of real zeros of polynomial of degree which are discussed in Monsi and Wolfe [1], Jamaludin et al [2][3][4][5][6], Monsi et al [7,8], Sham et al [9][10][11] and Bakar et al [12] are applied. The interval generated through the procedure in every step of the algorithm is decreasing in terms of width and guaranteed to still contain the zeros by inclusion of the intervals.…”