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

• 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; http://eprints.usm.my/48694/
• Institution: Universiti Sains Malaysia

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.