On the Interval Zoro Symmetric Single Step Procedure IZSS1-5D for the Simultaneous Bounding of Real Polynomial Zeros (original) (raw)

The Interval Zoro-Symmetric Single-Step IZSS1-5D for the Simultaneous Bounding of Real Polynomial Zeros

Malaysian Journal of Mathematical Sciences,9(2): 325-336.

A new modified method IZSS1-5D for the simultaneously bounding all the real zeros of a polynomial is formulated in this paper. The efficiency of this method is measured on the CPU times and the number of iterations after satisfying the convergence criteria where the results are obtained using five tested polynomials. The analysis performed shows that the R-order of convergence of this new procedure is at least five. The programming language used to obtain the numerical results is Matlab R2012, a software in association with Intlab V5.5 toolbox. The numerical results indicate that the procedure IZSS1-5D outperformed the IZSS1 in computational times and number of iterations.

An Efficient Interval Symmetric Single Step Procedure ISS1-5D for Simultaneous Bounding of Real Polynomial Zeros

International Journal of Mathematical Analysis

A new modified interval symmetric single-step procedure ISS1-5D which is the extension from the previous ISS1 is proposed. In procedure ISS1 we define informational efficiency of a method as the higher R-order of convergence evaluation. The procedure is tested on five test polynomials and the results are obtained using MATLAB 2007 software in association with IntLab V5.5 toolbox to record the CPU times and the number of iterations.

Modification on interval symmetric single-step procedure ISS-5δ for bounding polynomial zeros simultaneously

AIP Conference Proceedings

The purpose of this paper is to establish a new modified method. This modified procedure is called the Interval Symmetric Single Step-5 Delta Procedure ISS-5. This research start with some disjoints intervals as the initial intervals which contain the polynomial zeros. The procedure of ISS-5 will generate smaller bounded close intervals. The procedure is run on 5 test polynomials and the results obtained show that this procedure is more efficient than previous procedure.

Interval Symmetric Single-step Procedure ISS2-5D for Polynomial Zeros

Sains Malaysiana

We analyzed the rate of convergence of a new modified interval symmetric single-step procedure ISS2-5D which is an extension from the previous procedure ISS2. The algorithm of ISS2-5D includes the introduction of reusable correctors δi(k) (i = 1, …, n) for k ≥ 0. Furthermore, this procedure was tested on five test polynomials and the results were obtained using MATLAB 2007 software in association with IntLab V5.5 toolbox to record the CPU times and the number of iterations.

A modified interval symmetric single step procedure ISS-5D for simultaneous inclusion of polynomial zeros

AIP Conference Proceedings, 2013

The aim of this paper is to present a new modified interval symmetric single-step procedure ISS-5D which is the extension from the previous procedure, ISS1. The ISS-5D method will produce successively smaller intervals that are guaranteed to still contain the zeros. The efficiency of this method is measured on the CPU times and the number of iteration. The procedure is run on five test polynomials and the results obtained are shown in this paper.

On Modified Interval Symmetric Single-Step Procedure ISS2-5D for the Simultaneous Inclusion of Polynomial Zeros

International Journal of Mathematical Analysis

In this paper, we present a new modified interval symmetric single-step procedure ISS2-5D which is the extension from the previous procedure ISS2. The algorithm of ISS2-5D includes the introduction of reusable correctors (k ) (i 1,...,n) δ = for k ≥ 0 . The procedure is tested on five test polynomials and the results are obtained using MATLAB 2007 software in association with IntLab V5.5 toolbox to record the CPU times and the number of iterations.