Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros

Several modifications have been introduced in order to improve the problems in finding the zeros of polynomial simultaneously. They are named as Interval Symmetric Single-step 5-Delta procedure (ISS1-5D), Interval Midpoint Symmetric Single-step 5-Delta procedure (IMSS1-5D), Interval Zoro Symmetric S...

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Main Author:	Wan Mohd Sham, Atiyah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Interval analysis (Mathematics) Iterative methods (Mathematics) Convergence
Online Access:	http://psasir.upm.edu.my/id/eprint/55687/1/FS%202014%2038RR.pdf
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spelling	my-upm-ir.556872017-06-07T02:43:52Z Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros 2014-01 Wan Mohd Sham, Atiyah Several modifications have been introduced in order to improve the problems in finding the zeros of polynomial simultaneously. They are named as Interval Symmetric Single-step 5-Delta procedure (ISS1-5D), Interval Midpoint Symmetric Single-step 5-Delta procedure (IMSS1-5D), Interval Zoro Symmetric Single-step 5-Delta procedure (IZSS1-5D) and Interval Midpoint Zoro Symmetric Single-step 5-Delta procedure (IMZSS1-5D) which were explained in details in this thesis. These four new procedures have been established from the previous symmetric single-step procedure. Furthermore, we ensure that we start by choosing the suitable initial disjoint intervals which are guaranteed to contain one zero inside of each interval. The numerical results are given to validate the new modifications and the performances are being compared with the existing procedures in terms of number of iteration and computational time (CPU times). In addition, the convergence properties for all new modifications are investigated to ensure that the procedures are useful for finding the zeros of polynomial. The convergence analysis of each procedure is also discussed. The programming codes are developed and implemented using Matlab R2012b incorporated with Intlab V5.5 toolbox and compared with the existing procedures. The efficiency of the procedures is justified by the numerical results given. The results generated showed that these new procedures produced less computational time, higher rate of convergence and achieved the desired accuracy. Interval analysis (Mathematics) Iterative methods (Mathematics) Convergence 2014-01 Thesis http://psasir.upm.edu.my/id/eprint/55687/ http://psasir.upm.edu.my/id/eprint/55687/1/FS%202014%2038RR.pdf application/pdf en public masters Universiti Putra Malaysia Interval analysis (Mathematics) Iterative methods (Mathematics) Convergence
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Interval analysis (Mathematics) Iterative methods (Mathematics) Convergence
spellingShingle	Interval analysis (Mathematics) Iterative methods (Mathematics) Convergence Wan Mohd Sham, Atiyah Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
description	Several modifications have been introduced in order to improve the problems in finding the zeros of polynomial simultaneously. They are named as Interval Symmetric Single-step 5-Delta procedure (ISS1-5D), Interval Midpoint Symmetric Single-step 5-Delta procedure (IMSS1-5D), Interval Zoro Symmetric Single-step 5-Delta procedure (IZSS1-5D) and Interval Midpoint Zoro Symmetric Single-step 5-Delta procedure (IMZSS1-5D) which were explained in details in this thesis. These four new procedures have been established from the previous symmetric single-step procedure. Furthermore, we ensure that we start by choosing the suitable initial disjoint intervals which are guaranteed to contain one zero inside of each interval. The numerical results are given to validate the new modifications and the performances are being compared with the existing procedures in terms of number of iteration and computational time (CPU times). In addition, the convergence properties for all new modifications are investigated to ensure that the procedures are useful for finding the zeros of polynomial. The convergence analysis of each procedure is also discussed. The programming codes are developed and implemented using Matlab R2012b incorporated with Intlab V5.5 toolbox and compared with the existing procedures. The efficiency of the procedures is justified by the numerical results given. The results generated showed that these new procedures produced less computational time, higher rate of convergence and achieved the desired accuracy.
format	Thesis
qualification_level	Master's degree
author	Wan Mohd Sham, Atiyah
author_facet	Wan Mohd Sham, Atiyah
author_sort	Wan Mohd Sham, Atiyah
title	Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
title_short	Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
title_full	Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
title_fullStr	Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
title_full_unstemmed	Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
title_sort	modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/55687/1/FS%202014%2038RR.pdf
_version_	1747812109095272448

Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros

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