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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.

The rate of convergence of the interval symmetric single-step procedure IMW is increased by introducing a Newton’s method (NM) at the beginning of the procedure. The numerical convergence of this new procedure called INSMW is shown. Based on the numerical results, this new procedure performed better than does IMW, verifying the rate of convergence to be at least four.

The point symmetric single-step procedure PSS1 has R-order of convergence at least three. This method is modified, and calledthe 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.

This paper describes the Interval Zoro-Symmetric Single-Step Procedure IZSS2-5D which is an extension of the previously proposed procedure IZSS2. It is also an extension of our procedure ISS2-5D. This procedure is developed in order to enhance the rate of convergence. Numerical results are obtained and they indicated that the IZSS2-5D outperformed the ISS2-5D in terms of computational time and number of iterations.

A new modified method IZSS1-5D for the simultaneously bounding all the 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 test polynomials. The R-order of convergence of this method is at least five.

A new method called the interval zoro symmetric single-step procedure IZSS2-5D which is an extension of the previous procedure IZSS2 is described. The numerical results using five test polynomials contributed to shorter CPU times and reduced number of iterations.

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.

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.

We develop, formulate, verify and later validate a multiobjective model of student admission. Through a two-stage optimization procedure the model seeks to maximize student admission and student allocation into departments and academic programmes respectively. In the first stage, we seek to determine the optimal number of new student intake in all the departments of a given faculty by observing the departments’ capacity limitations in terms of lecture rooms/halls availability, budget constraints, number of faculty members and affirmative action quota. The second stage concerns the application of the same procedure with the objective of determining the optimal allocation of students obtained in the first stage into the respective academic programmes within the same department with constraints unique to each academic programme. Every constraint has its own weightage besides its level of priority. We then describe the application of the model to the Faculty of Science & Technology of the Universiti Kebangsaan Malaysia with its five academic centres/departments and then to the Centre for Mathematical Sciences with its three academic programmes. For both stages, we compare the results of the preemptive goal programming model with the non preemptive weighted goal programming model to analyse the adaptability of the models to real situations. Sensitivity analyses of the results are done to gauge the reliability of the model. We hope that the results of the application will demonstrate the model’s capability to provide an optimal apportionment of student admission policy with regard to the number of student intake and allocation into the departmental academic programmes of a faculty, as well as recognizing the capacity limitations of each academic programme.