Chebyshev approximation of discrete polynomials and splines

This work is concerned with the approximation of discrete data using polynomials and splines based on the Chebyshev approximation criterion. Five algorithms are proposed in this work to implement the Chebyshev approximation criterion. These algorithms use either cubic splines or Lagrange polyn...

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Main Author:	Che Seman, Fauziahanim
Format:	Thesis
Language:	English English English
Published:	2004
Subjects:	QA Mathematics QA150-272.5 Algebra
Online Access:	http://eprints.uthm.edu.my/8155/1/24p%20FAUZIAHANIM%20CHE%20SEMAN.pdf http://eprints.uthm.edu.my/8155/2/FAUZIAHANIM%20CHE%20SEMAN%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/8155/3/FAUZIAHANIM%20CHE%20SEMAN%20WATERMARK.pdf
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id	my-uthm-ep.8155
record_format	uketd_dc
spelling	my-uthm-ep.81552023-01-17T03:44:02Z Chebyshev approximation of discrete polynomials and splines 2004-09 Che Seman, Fauziahanim QA Mathematics QA150-272.5 Algebra This work is concerned with the approximation of discrete data using polynomials and splines based on the Chebyshev approximation criterion. Five algorithms are proposed in this work to implement the Chebyshev approximation criterion. These algorithms use either cubic splines or Lagrange polynomials to construct the approximation function. The efficiency of each algorithm developed is evaluated on the basis of the number of iterations and extreme points required for convergence, and the magnitude of the errors generated. One measure of efficiency is the minimum number of knots required to capture the full behavior of the data, and the size of the error between the actual data and its approximation. These knots are the extreme points that determine how well the fitting function approximates the actual data. Since a critical step in the approximation is identifying the extreme points, in this work we have proposed a novel procedure for finding the set of extreme points for the incoming discrete data efficiently. The procedure developed in this work use polynomials and cubic splines to construct the approximation function. The output of the algorithm is a set of extreme points that can be used to construct a minimal error approximation function. A total of five algorithms based on the Lagrange polynomials and cubic splines have been developed in this work to identify the extreme points. The efficiency of each algorithm is analysed in terms of computation time and the magnitude of the errors generated. In real environment, it is hope that this theoretical work can be applied to actual data and solves problems which occur in data processing. 2004-09 Thesis http://eprints.uthm.edu.my/8155/ http://eprints.uthm.edu.my/8155/1/24p%20FAUZIAHANIM%20CHE%20SEMAN.pdf text en public http://eprints.uthm.edu.my/8155/2/FAUZIAHANIM%20CHE%20SEMAN%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/8155/3/FAUZIAHANIM%20CHE%20SEMAN%20WATERMARK.pdf text en validuser mphil masters Kolej Universiti Teknologi Tun Hussein Onn Fakulti Kejuruteraan Elektrik
institution	Universiti Tun Hussein Onn Malaysia
collection	UTHM Institutional Repository
language	English English English
topic	QA Mathematics QA150-272.5 Algebra
spellingShingle	QA Mathematics QA150-272.5 Algebra Che Seman, Fauziahanim Chebyshev approximation of discrete polynomials and splines
description	This work is concerned with the approximation of discrete data using polynomials and splines based on the Chebyshev approximation criterion. Five algorithms are proposed in this work to implement the Chebyshev approximation criterion. These algorithms use either cubic splines or Lagrange polynomials to construct the approximation function. The efficiency of each algorithm developed is evaluated on the basis of the number of iterations and extreme points required for convergence, and the magnitude of the errors generated. One measure of efficiency is the minimum number of knots required to capture the full behavior of the data, and the size of the error between the actual data and its approximation. These knots are the extreme points that determine how well the fitting function approximates the actual data. Since a critical step in the approximation is identifying the extreme points, in this work we have proposed a novel procedure for finding the set of extreme points for the incoming discrete data efficiently. The procedure developed in this work use polynomials and cubic splines to construct the approximation function. The output of the algorithm is a set of extreme points that can be used to construct a minimal error approximation function. A total of five algorithms based on the Lagrange polynomials and cubic splines have been developed in this work to identify the extreme points. The efficiency of each algorithm is analysed in terms of computation time and the magnitude of the errors generated. In real environment, it is hope that this theoretical work can be applied to actual data and solves problems which occur in data processing.
format	Thesis
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Che Seman, Fauziahanim
author_facet	Che Seman, Fauziahanim
author_sort	Che Seman, Fauziahanim
title	Chebyshev approximation of discrete polynomials and splines
title_short	Chebyshev approximation of discrete polynomials and splines
title_full	Chebyshev approximation of discrete polynomials and splines
title_fullStr	Chebyshev approximation of discrete polynomials and splines
title_full_unstemmed	Chebyshev approximation of discrete polynomials and splines
title_sort	chebyshev approximation of discrete polynomials and splines
granting_institution	Kolej Universiti Teknologi Tun Hussein Onn
granting_department	Fakulti Kejuruteraan Elektrik
publishDate	2004
url	http://eprints.uthm.edu.my/8155/1/24p%20FAUZIAHANIM%20CHE%20SEMAN.pdf http://eprints.uthm.edu.my/8155/2/FAUZIAHANIM%20CHE%20SEMAN%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/8155/3/FAUZIAHANIM%20CHE%20SEMAN%20WATERMARK.pdf
_version_	1776103288544952320

Chebyshev approximation of discrete polynomials and splines

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