Sains Malaysiana 43(7)(2014): 1101–1104

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

(Prosedur Selang Bersimetri Langkah-tunggal ISS2-5D untuk Punca Polinomial)

NORAINI JAMALUDIN¹, MANSOR MONSI¹ & NASRUDDIN HASSAN²*

¹Mathematics Department, Faculty of Science, Universiti Putra Malaysia

43400 Serdang, Selangor, D.E. Malaysia

²School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Diserahkan: 24 Jun 2013/Diterima: 14 Oktober 2013

ABSTRACT

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.

Keywords: Interval procedure; polynomial zeros; rate of convergence; simultaneous inclusion; symmetric single-step

ABSTRAK

Satu analisis dilakukan terhadap kadar penumpuan bagi prosedur terubahsuai selang bersimetri langkah-tunggal ISS2-5D baru yang merupakan lanjutan daripada prosedur ISS2 sebelumnya. Algoritma ISS2-5D termasuk pengenalan pembetulan yang boleh diguna semula δi(k) (i = 1, …, n) untuk k ≥ 0. Prosedur ini diuji ke atas lima jenis polinomial dan keputusan diperoleh menggunakan perisian MATLAB 2007 dan peralatan IntLab V5.5 untuk merekod masa CPU dan bilangan lelaran.

Kata kunci: Kadar penumpuan; kemasukan serentak; prosedur selang; punca polinomial; selang langkah tunggal bersimetri

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*Pengarang untuk surat-menyurat; email: nas@ukm.edu.my