Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros

The purpose of this thesis is to find the inclusion of polynomial zeros by using interval analysis approach. We will focus on interval single-step method in order to gain the fastest speed of convergence for bounding simple polynomial zeros simultaneously. Firstly, we will generally describe on some...

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Main Author:	Salim, Nur Raidah
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Symmetry Polynomials Interval analysis (Mathematics)
Online Access:	http://psasir.upm.edu.my/id/eprint/32224/1/FS%202012%2021R.pdf
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spelling	my-upm-ir.322242015-01-19T05:21:18Z Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros 2012-01 Salim, Nur Raidah The purpose of this thesis is to find the inclusion of polynomial zeros by using interval analysis approach. We will focus on interval single-step method in order to gain the fastest speed of convergence for bounding simple polynomial zeros simultaneously. Firstly, we will generally describe on some basic mathematical background on interval analysis approach. Then, we will briefly discuss the procedure given in the literature which has been proved by other researchers. We present some information on interval single-step IS method together with the algorithm and the analysis on the rate of convergence. In order to improve IS method, we made several modifications using interval analysis approaches whereby it has been proved that these procedures not only including intervals for roots, but also convergent under a few assumptions. We have new modification namely ISS, IZSS and IZMSS methods which are describe precisely in this thesis. The processing time (CPU) of the algorithm of the modified methods may be done using Matlab 2007a associated with Intlab. Nevertheless, we will also present the theoretical analyses of the convergence rate of the modified procedure. This thesis will cover the algorithms, theoretical analysis and numerical results for each modification. Based on the analysis that has been done, we finally found the rate of convergence for ISS is at least 9, for IZSS is at least 13 and for IMZSS is at least 16 while the rate of convergence of IS is at least 2(1+r)˃3. Finally, we conclude our thesis by comparing all the factors needed in a table and we give some possible extensions for future works. Symmetry Polynomials Interval analysis (Mathematics) 2012-01 Thesis http://psasir.upm.edu.my/id/eprint/32224/ http://psasir.upm.edu.my/id/eprint/32224/1/FS%202012%2021R.pdf application/pdf en public masters Universiti Putra Malaysia Symmetry Polynomials Interval analysis (Mathematics) Faculty of Science
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Symmetry Polynomials Interval analysis (Mathematics)
spellingShingle	Symmetry Polynomials Interval analysis (Mathematics) Salim, Nur Raidah Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
description	The purpose of this thesis is to find the inclusion of polynomial zeros by using interval analysis approach. We will focus on interval single-step method in order to gain the fastest speed of convergence for bounding simple polynomial zeros simultaneously. Firstly, we will generally describe on some basic mathematical background on interval analysis approach. Then, we will briefly discuss the procedure given in the literature which has been proved by other researchers. We present some information on interval single-step IS method together with the algorithm and the analysis on the rate of convergence. In order to improve IS method, we made several modifications using interval analysis approaches whereby it has been proved that these procedures not only including intervals for roots, but also convergent under a few assumptions. We have new modification namely ISS, IZSS and IZMSS methods which are describe precisely in this thesis. The processing time (CPU) of the algorithm of the modified methods may be done using Matlab 2007a associated with Intlab. Nevertheless, we will also present the theoretical analyses of the convergence rate of the modified procedure. This thesis will cover the algorithms, theoretical analysis and numerical results for each modification. Based on the analysis that has been done, we finally found the rate of convergence for ISS is at least 9, for IZSS is at least 13 and for IMZSS is at least 16 while the rate of convergence of IS is at least 2(1+r)˃3. Finally, we conclude our thesis by comparing all the factors needed in a table and we give some possible extensions for future works.
format	Thesis
qualification_level	Master's degree
author	Salim, Nur Raidah
author_facet	Salim, Nur Raidah
author_sort	Salim, Nur Raidah
title	Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
title_short	Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
title_full	Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
title_fullStr	Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
title_full_unstemmed	Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
title_sort	convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/32224/1/FS%202012%2021R.pdf
_version_	1747811650859171840

Convergence of interval symmetric single-step method for simultaneous inclusion of real polynomial zeros

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