Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials

In this thesis, we discuss about the interval iterative procedures of bounding real zeros of polynomials simultaneously. We concentrate on the procedure that has been proposed by Monsi in 1988 that is the interval symmetric single-step procedure ISS1 and do some modifications on the procedure and co...

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Main Author:	Mohammad Rusli, Syaida Fadhilah
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Polynomials Interval analysis (Mathematics)
Online Access:	http://psasir.upm.edu.my/id/eprint/20858/1/FS_2011_53_IR.pdf
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spelling	my-upm-ir.208582022-01-26T04:35:53Z Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials 2011-10 Mohammad Rusli, Syaida Fadhilah In this thesis, we discuss about the interval iterative procedures of bounding real zeros of polynomials simultaneously. We concentrate on the procedure that has been proposed by Monsi in 1988 that is the interval symmetric single-step procedure ISS1 and do some modifications on the procedure and come out with three modified procedures. For these procedures, we start with suitably chosen initial disjoint intervals where each interval contains a zero of a polynomial. These procedures will produce successively smaller intervals that are guaranteed to still contain the zeros. In order to assure that the procedures are promising, we analyze the R-order of convergence of the procedures and compare them with the original procedure ISS1. We include the analysis of inclusions to certify the convergences of the procedures. The coding for the algorithms of these procedures are developed and implemented using the MATLAB R2007a in co-operated with the Intlab V5.5 toolbox for interval arithmetic developed by Rump. These three new modified procedures are proved to have better rate of convergences and this is supported by lesser CPU times and lesser number of iterations. Polynomials Interval analysis (Mathematics) 2011-10 Thesis http://psasir.upm.edu.my/id/eprint/20858/ http://psasir.upm.edu.my/id/eprint/20858/1/FS_2011_53_IR.pdf application/pdf en public masters Universiti Putra Malaysia Polynomials Interval analysis (Mathematics) Faculty of Sciences English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Polynomials Interval analysis (Mathematics)
spellingShingle	Polynomials Interval analysis (Mathematics) Mohammad Rusli, Syaida Fadhilah Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
description	In this thesis, we discuss about the interval iterative procedures of bounding real zeros of polynomials simultaneously. We concentrate on the procedure that has been proposed by Monsi in 1988 that is the interval symmetric single-step procedure ISS1 and do some modifications on the procedure and come out with three modified procedures. For these procedures, we start with suitably chosen initial disjoint intervals where each interval contains a zero of a polynomial. These procedures will produce successively smaller intervals that are guaranteed to still contain the zeros. In order to assure that the procedures are promising, we analyze the R-order of convergence of the procedures and compare them with the original procedure ISS1. We include the analysis of inclusions to certify the convergences of the procedures. The coding for the algorithms of these procedures are developed and implemented using the MATLAB R2007a in co-operated with the Intlab V5.5 toolbox for interval arithmetic developed by Rump. These three new modified procedures are proved to have better rate of convergences and this is supported by lesser CPU times and lesser number of iterations.
format	Thesis
qualification_level	Master's degree
author	Mohammad Rusli, Syaida Fadhilah
author_facet	Mohammad Rusli, Syaida Fadhilah
author_sort	Mohammad Rusli, Syaida Fadhilah
title	Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
title_short	Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
title_full	Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
title_fullStr	Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
title_full_unstemmed	Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials
title_sort	some modification on interval symmetric single-step procedure for simultaneous inclusion of real zzeros of polynomials
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Sciences
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/20858/1/FS_2011_53_IR.pdf
_version_	1747811478091595776

Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials

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