Rational cubic spline for preserving the positivity of 3D positive data

2016 ◽  
Author(s):  
Anas Khalaf Faris ◽  
Zainor Ridzuan Yahya ◽  
Nursalasawati Rusli ◽  
Nur’Afifah Rusdi
Keyword(s):  
Cubic Spline ◽  
Positive Data

scholarly journals Shape Preserving Interpolation UsingC2Rational Cubic Spline

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Kong Voon Pang
Keyword(s):  
Spline Interpolation ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Cubic Spline ◽  
Shape Preserving ◽  
Cubic Spline Interpolation ◽  
Positive Data ◽  
Shape Preserving Interpolation ◽  
Systems Of Linear Equations ◽  
Two Parameters

This paper discusses the construction of newC2rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parametersαi,βi, andγi. The sufficient conditions for the positivity are derived on one parameterγiwhile the other two parametersαiandβiare free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation withC2continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion andC2continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivativesdi,i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the newC2rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated isft∈C3t0,tnis also investigated in detail.

Glucose Calibration Modeling in Blood with Spline Regression Approaching to Non-Invasive Tools

2018 ◽  
pp. 144-149
Author(s):  
Ria Hayatun Nur ◽  
Indahwati A ◽  
Erfiani A
Keyword(s):  
Diabetes Mellitus ◽  
Linear Regression ◽  
Good Health ◽  
Cubic Spline ◽  
The Body ◽  
Spline Regression ◽  
Linear Quadratic ◽  
Important Thing ◽  
Non Invasive

In this globalization era, health is the most important thing to be able to run various activities. Without good health, this will hinder many activities. Diabetes mellitus is one of the diseases caused by unhealty lifestyle.There are many treatments that can be done to prevent the occurrence of diabetes. The treatments are giving the insulin and also checking the glucose rate to the patients.Checking the glucose rate needs the tools which is safety to the body. This research want to develop non invasive tool which is safety and do not injure the patient. The purpose of this research is also finding the best model which derived from Linear, Quadratic, and Cubic Spline Regression. Some respondents were taking to get the glucose measuring by invasive and non invasive tools. It could be seen clearly that Spline Linear Regression was the best model than Quadratic and Cubic Spline Regression. It had 70% and 33.939 for R2 and RMSEP respectively.

ACCURACY OF RIVER GEOMETRY INTERPOLATION USING CUBIC SPLINE CURVE AT ALB MISSING AREA AND INFULUENCE OF FLOW REGIME

2018 ◽  
Vol 74 (4) ◽  
pp. I_859-I_864
Author(s):  
Takayuki OKABE ◽  
Takanori YAMAZAKI ◽  
Atsumasa OZAWA ◽  
Shinichi MORITA ◽  
Shigeo HORIUCHI ◽  
...  
Keyword(s):  
Flow Regime ◽  
Cubic Spline ◽  
Spline Curve ◽  
Cubic Spline Curve
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