On modified symmetric single-step procedure for estimating polynomial zeros simultaneously

Abstract

The point symmetric single-step procedure PSS1 has R-order of convergence at least three. This method is modified, and called the midpoint symmetric single-step procedure PMSS1, so that a better rate of convergence is achieved. The convergence analysis of PMSS1 is shown along with its numerical results.

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.…”