An algorithm for the simultaneous inclusion of real polynomial zeros

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…”

“…Interval iterative procedure for simultaneous inclusion of simple polynomial zeros were discussed in [12,5,3,9,8]. In this paper, we consider the ideas of [4,2,11,13] and these ideas are to be used in the IZSS2-5D procedure.…”

“…In this paper, we consider the ideas of [4,2,11,13] and these ideas are to be used in the IZSS2-5D procedure. This procedure needs some pre-conditions for initial intervals (0) ( 1,..., ) i X i n to converge to the zeros * ( 1,..., ) i x i n respectively (see Monsi and Wolfe [8] and Monsi [15]), starting with some disjoints intervals (0) ( 1,..., ) i X i n each of which contains a polynomial zero. It will produce bounded closed intervals where each will trap the required zero.…”

“…The backward step of this procedure comes from the idea of [8]. Meanwhile the second forward step is taken from the idea of [13].…”

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.…”