Syaida Fadhilah Mohammad Rusli

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

The point symmetric single step procedure PSS1 has R-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 the R-order of convergence of PZSS1 is at least 4 which is higher than the R-order of convergence of PT1, PS1, and PSS1. Hence, computational time is reduced since this procedure is more efficient for bounding simple zeros simultaneously.

On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously

We present a new rapidly convergence procedure called the interval repeated zoro symmetric single-step IRZSS1-5D which is an extension of the procedures IZSS1-5D and IRSS1. Theoretical analysis shows that the rate of convergence of IRZSS1-5D is at least 3r + 2 (r ≥ 1), whereas the rates of convergence of IZSS1-5D and IRSS1 are at least five and 2r + 1 (r ≥ 1), respectively. With r = 1, the procedure IRZSS1-5D is identical to IZSS1-5D. The procedures IRSS1 and IZSS1-5D are the basic references for the establishment of IRZSS1-5D, where the forward-backward-forward (FBF) step of IZSS1-5D are repeated r times in IRZSS1-5D, so that some elements of FBF of IZSS1-5D can be saved and reused for the next inner iterations r = 2,3, … in IRZSS1-5D.

On the convergence rate of interval repeated midpoint zoro symmetric single-step procedure for simultaneous bounding the polynomial zeros

In this paper, we present the analysis of the rate of convergence of the interval repeated midpoint zoro symmetric single-step procedure (IRMZSS) which is the extension of the interval midpoint zoro symmetric single-step procedure (IMZSS). The results show that the procedure IRMZSS has R-order of convergence at least 7r + 1 (r ≥ 1) or 0R (IRMZSS) ≥ 7 r + 1 (r ≥ 1), whereas the procedure IMZSS R-order of convergence at least 8 or 0R (IMZSS) ≥ 8. In fact 0R (IRMZSS) ≥ 0R (IMZSS) and 0R (IRMZSS) = 0R (IRMZSS) = 0R (IMZSS) when r = 1.