Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros

The focus of this research is on the bounding of simple and real polynomial zeros simultaneously, focusing on the interval analysis approaches. This procedure started with some disjoint intervals XXXX each of which contains a zero of the polynomial and finally produced successively smaller closed bo...

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Main Author:	Jamaludin, Noraini
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Polynomials Convergence Equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/55668/1/FS%202014%2033RR.pdf
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id	my-upm-ir.55668
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spelling	my-upm-ir.556682017-06-07T01:50:41Z Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros 2014-01 Jamaludin, Noraini The focus of this research is on the bounding of simple and real polynomial zeros simultaneously, focusing on the interval analysis approaches. This procedure started with some disjoint intervals XXXX each of which contains a zero of the polynomial and finally produced successively smaller closed bounded intervals, which always converge XX to the zeros for XXXX respectively. In relation to that, the previous work on Interval Symmetric Single-step (ISS2) procedure is investigated to ensure this procedure is useful for solving polynomials. Thus, this procedure is extended to some modifications in order to improve the efficiency of the procedure. Starting from the authentic ISS2 procedure, four modified procedures are developed. The procedures are Interval Symmetric Single-Step (ISS2-5D) procedure, Interval Zoro-Symmetric Single-Step (IZSS2-5D) procedure,Interval Midpoint Symmetric Single-Step (IMSS2-5D) procedure and Interval Midpoint Zoro-Symmetric Single-Step (IMZSS2-5D) procedure. The programming language Intlab toolbox for Matlab is used to record the numerical results, whereby the stopping criterion used is XXXX 10−10. The results are numerically compared to the original ISS2 procedure to supervise the improvements and efficiencies of the modified procedures. In order to assure that the outcomes of the procedures are promising,convergence rate for each modified procedures is analyzed for comparing purposes. Other than that, the analysis of inclusion to certify the convergence of the modified procedures is included. All the modifications are proven to have better rate of convergences and these are well-supported on the reduction of CPU times, number of iterations and the value of the interval width of the procedures. In a nutshell, this study reveals that the new modified procedures are capable and efficient for bounding the simple and real polynomial zeros simultaneously. Polynomials Convergence Equations - Numerical solutions 2014-01 Thesis http://psasir.upm.edu.my/id/eprint/55668/ http://psasir.upm.edu.my/id/eprint/55668/1/FS%202014%2033RR.pdf application/pdf en public masters Universiti Putra Malaysia Polynomials Convergence Equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Polynomials Convergence Equations - Numerical solutions
spellingShingle	Polynomials Convergence Equations - Numerical solutions Jamaludin, Noraini Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
description	The focus of this research is on the bounding of simple and real polynomial zeros simultaneously, focusing on the interval analysis approaches. This procedure started with some disjoint intervals XXXX each of which contains a zero of the polynomial and finally produced successively smaller closed bounded intervals, which always converge XX to the zeros for XXXX respectively. In relation to that, the previous work on Interval Symmetric Single-step (ISS2) procedure is investigated to ensure this procedure is useful for solving polynomials. Thus, this procedure is extended to some modifications in order to improve the efficiency of the procedure. Starting from the authentic ISS2 procedure, four modified procedures are developed. The procedures are Interval Symmetric Single-Step (ISS2-5D) procedure, Interval Zoro-Symmetric Single-Step (IZSS2-5D) procedure,Interval Midpoint Symmetric Single-Step (IMSS2-5D) procedure and Interval Midpoint Zoro-Symmetric Single-Step (IMZSS2-5D) procedure. The programming language Intlab toolbox for Matlab is used to record the numerical results, whereby the stopping criterion used is XXXX 10−10. The results are numerically compared to the original ISS2 procedure to supervise the improvements and efficiencies of the modified procedures. In order to assure that the outcomes of the procedures are promising,convergence rate for each modified procedures is analyzed for comparing purposes. Other than that, the analysis of inclusion to certify the convergence of the modified procedures is included. All the modifications are proven to have better rate of convergences and these are well-supported on the reduction of CPU times, number of iterations and the value of the interval width of the procedures. In a nutshell, this study reveals that the new modified procedures are capable and efficient for bounding the simple and real polynomial zeros simultaneously.
format	Thesis
qualification_level	Master's degree
author	Jamaludin, Noraini
author_facet	Jamaludin, Noraini
author_sort	Jamaludin, Noraini
title	Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
title_short	Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
title_full	Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
title_fullStr	Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
title_full_unstemmed	Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
title_sort	modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/55668/1/FS%202014%2033RR.pdf
_version_	1747812107885215744

Modification of interval symmetric single-step procedure for simultaneous bounding polynomial zeros

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