Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function

In this thesis, a rational cubic Bézier-Ball function which refers to a rational cubic Bézier function expressed in terms of Ball control points and weights are used to preserve positivity and monotonicity of real data sets. Four shape parameters are proposed to preserve the characteristics of th...

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Main Author:	Ahmad, Afida
Format:	Thesis
Language:	English
Published:	2018
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/48694/1/AFIDA%20BINTI%20AHMAD_hj.pdf
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id	my-usm-ep.48694
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spelling	my-usm-ep.486942021-03-26T07:12:09Z Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function 2018-08 Ahmad, Afida QA1 Mathematics (General) In this thesis, a rational cubic Bézier-Ball function which refers to a rational cubic Bézier function expressed in terms of Ball control points and weights are used to preserve positivity and monotonicity of real data sets. Four shape parameters are proposed to preserve the characteristics of the data. A rational Bi-Cubic Bézier-Ball function is introduced to preserve the positivity of surface generated from real data set and from known functions. Eight shape parameters proposed can be modified to preserve the positivity of the surface. Interpolating 2D and 3D real data using radial basis function (RBF) is proposed as an alternative method to preserve the positivity of the data. Two types of RBF which are Multiquadric (MQ) function and Gaussian function, which contains a shape parameter are used. The boundaries (lower and upper limit) of the shape parameter which preserves the positivity of real data are proposed. Comparisons are made using the root-mean-square (RMS) error between the proposed interpolation methods with existing works in literature. It was found that MQ function and rational cubic Bézier-Ball is comparable with existing literature in preserving positivity for both curves and surfaces. For preserving monotonicity, the rational cubic Bézier-Ball is comparable but the MQ quasi-interpolation introduced can only linearly interpolate the curve and the RMS values are big. Gaussian function is able to preserve positivity of curves and surfaces but with unwanted oscillations which result to unsmooth curves. 2018-08 Thesis http://eprints.usm.my/48694/ http://eprints.usm.my/48694/1/AFIDA%20BINTI%20AHMAD_hj.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1 Mathematics (General)
spellingShingle	QA1 Mathematics (General) Ahmad, Afida Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
description	In this thesis, a rational cubic Bézier-Ball function which refers to a rational cubic Bézier function expressed in terms of Ball control points and weights are used to preserve positivity and monotonicity of real data sets. Four shape parameters are proposed to preserve the characteristics of the data. A rational Bi-Cubic Bézier-Ball function is introduced to preserve the positivity of surface generated from real data set and from known functions. Eight shape parameters proposed can be modified to preserve the positivity of the surface. Interpolating 2D and 3D real data using radial basis function (RBF) is proposed as an alternative method to preserve the positivity of the data. Two types of RBF which are Multiquadric (MQ) function and Gaussian function, which contains a shape parameter are used. The boundaries (lower and upper limit) of the shape parameter which preserves the positivity of real data are proposed. Comparisons are made using the root-mean-square (RMS) error between the proposed interpolation methods with existing works in literature. It was found that MQ function and rational cubic Bézier-Ball is comparable with existing literature in preserving positivity for both curves and surfaces. For preserving monotonicity, the rational cubic Bézier-Ball is comparable but the MQ quasi-interpolation introduced can only linearly interpolate the curve and the RMS values are big. Gaussian function is able to preserve positivity of curves and surfaces but with unwanted oscillations which result to unsmooth curves.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ahmad, Afida
author_facet	Ahmad, Afida
author_sort	Ahmad, Afida
title	Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
title_short	Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
title_full	Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
title_fullStr	Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
title_full_unstemmed	Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function
title_sort	preserving positivity and monotonicity of real data using bézier-ball function and radial basis function
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2018
url	http://eprints.usm.my/48694/1/AFIDA%20BINTI%20AHMAD_hj.pdf
_version_	1747821962117251072

Preserving Positivity And Monotonicity Of Real Data Using Bézier-Ball Function And Radial Basis Function

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