Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable

The main objective of this thesis is to find a zero of a function using interval analysis approach. Specifically, the focus is on the well-known method called interval parameter regula falsi method (p-RF). Three modifications had been made in order to improve the p-RF method. The new modifications...

Full description

Saved in:

Bibliographic Details
Main Author:	Abu Bakar, Norhaliza
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Algorithms Interval analysis (Mathematics)
Online Access:	http://psasir.upm.edu.my/id/eprint/31938/1/FS%202012%2038R.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.31938
record_format	uketd_dc
spelling	my-upm-ir.319382015-05-19T06:48:47Z Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable 2012-01 Abu Bakar, Norhaliza The main objective of this thesis is to find a zero of a function using interval analysis approach. Specifically, the focus is on the well-known method called interval parameter regula falsi method (p-RF). Three modifications had been made in order to improve the p-RF method. The new modifications namely p-RFM1, p-RFM2 and p-RFM3 methods were described widely in this thesis. This study also considers the average of central processing unit (CPU) time of the algorithms of the modified methods where they were ran on Matlab R2007a software in associated with Intlab package. The theoretical analysis of the convergence rate of the modi¯ed methods were given. The p-RFM1 method is focusing on updating the midpoint of current interval in the inner iteration i. Another inner iteration l was introduced in p-RFM1 and the name of this modification is p-RFM2 method. The calculation of the gradient of the function in the p-RFM1 method is approximated using the secant method. The actual gradient of the current midpoint is now replacing the approximated gradient. The modification was named as the p-RFM3 method. All the modified methods mentioned above showed better rate of convergence than p-RF method. This is supported by lesser average CPU times tested on nine test problems. Therefore, it is concluded that the modified methods are better in term of rate of convergence and average CPU time than the original method. Algorithms Interval analysis (Mathematics) Equations, Roots of 2012-01 Thesis http://psasir.upm.edu.my/id/eprint/31938/ http://psasir.upm.edu.my/id/eprint/31938/1/FS%202012%2038R.pdf application/pdf en public masters Universiti Putra Malaysia Algorithms Interval analysis (Mathematics) Equations, Roots of Faculty of Science
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Algorithms Interval analysis (Mathematics) Algorithms
spellingShingle	Algorithms Interval analysis (Mathematics) Algorithms Abu Bakar, Norhaliza Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
description	The main objective of this thesis is to find a zero of a function using interval analysis approach. Specifically, the focus is on the well-known method called interval parameter regula falsi method (p-RF). Three modifications had been made in order to improve the p-RF method. The new modifications namely p-RFM1, p-RFM2 and p-RFM3 methods were described widely in this thesis. This study also considers the average of central processing unit (CPU) time of the algorithms of the modified methods where they were ran on Matlab R2007a software in associated with Intlab package. The theoretical analysis of the convergence rate of the modi¯ed methods were given. The p-RFM1 method is focusing on updating the midpoint of current interval in the inner iteration i. Another inner iteration l was introduced in p-RFM1 and the name of this modification is p-RFM2 method. The calculation of the gradient of the function in the p-RFM1 method is approximated using the secant method. The actual gradient of the current midpoint is now replacing the approximated gradient. The modification was named as the p-RFM3 method. All the modified methods mentioned above showed better rate of convergence than p-RF method. This is supported by lesser average CPU times tested on nine test problems. Therefore, it is concluded that the modified methods are better in term of rate of convergence and average CPU time than the original method.
format	Thesis
qualification_level	Master's degree
author	Abu Bakar, Norhaliza
author_facet	Abu Bakar, Norhaliza
author_sort	Abu Bakar, Norhaliza
title	Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
title_short	Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
title_full	Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
title_fullStr	Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
title_full_unstemmed	Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable
title_sort	modifications of parameter regula falsi method p-rf for inclusion of zero of a function with one real variable
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/31938/1/FS%202012%2038R.pdf
_version_	1747811636344782848

Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable

Similar Items