Write a MatLab user-defined function that determines the coefficients of a cubic polynomial, ƒ(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and y are vectors with the coordinates of the data points, and the output argument a is a four-element vector with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error. (a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture slides): Curve fitting - polynomial regression - Example A tension test is conducted for determining the stress-strain be- havior of rubber. The data points from the test are shown in the figure, and their values are given below. Determine the fourth order polynomial that best fits the data points. Make a plot of the data points and the curve that corresponds to the polynomial. Strain € Stress o (MPa) Strain € Stress o (MPa) 0 0.4 0.8 1.2 1.6 2.0 2.4 0 3.0 4.5 5.8 5.9 5.8 6.2 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 7.4 9.6 15.6 20.7 26.7 31.1 35.6 39.3 41.5 40 36 Strain 6 6 2 (b) Write a program in a script file that plots the data points and the curve of the cubic polynomial that best fits the data.
Write a MatLab user-defined function that determines the coefficients of a cubic polynomial, ƒ(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and y are vectors with the coordinates of the data points, and the output argument a is a four-element vector with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error. (a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture slides): Curve fitting - polynomial regression - Example A tension test is conducted for determining the stress-strain be- havior of rubber. The data points from the test are shown in the figure, and their values are given below. Determine the fourth order polynomial that best fits the data points. Make a plot of the data points and the curve that corresponds to the polynomial. Strain € Stress o (MPa) Strain € Stress o (MPa) 0 0.4 0.8 1.2 1.6 2.0 2.4 0 3.0 4.5 5.8 5.9 5.8 6.2 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 7.4 9.6 15.6 20.7 26.7 31.1 35.6 39.3 41.5 40 36 Strain 6 6 2 (b) Write a program in a script file that plots the data points and the curve of the cubic polynomial that best fits the data.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
![Write a MatLab user-defined function that determines the coefficients of a cubic polynomial,
f(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also
calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and
y are vectors with the coordinates of the data points, and the output argument a is a four-element vector
with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error.
"
(a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture
slides):
Curve fitting - polynomial regression - Example
A tension test is conducted for determining the stress-strain be-
havior of rubber. The data points from the test are shown in the
figure, and their values are given below. Determine the fourth
order polynomial that best fits the data points. Make a plot of
the data points and the curve that corresponds to the polynomial.
Strain €
0 0.4 0.8 1.2 1.6 2.0 2.4
Stress (MPa) 0 3.0 4.5 5.8 5.9 5.8 6.2
Strain €
Stress (MPa)
2.8 3.2 3.6
7.4 9.6 15.6 20.7
4.0 4.4 4.8 5.2 5.6 6.0
26.7 31.1 35.6 39.3 41.5
36
Strain
192
(b) Write a program in a script file that plots the data points and the curve of the cubic polynomial that
best fits the data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4908425-6b77-4ea0-88fa-d88faee532f6%2Fe521089c-5571-4fab-bf87-8e8b019740ad%2F7sdhyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Write a MatLab user-defined function that determines the coefficients of a cubic polynomial,
f(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also
calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and
y are vectors with the coordinates of the data points, and the output argument a is a four-element vector
with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error.
"
(a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture
slides):
Curve fitting - polynomial regression - Example
A tension test is conducted for determining the stress-strain be-
havior of rubber. The data points from the test are shown in the
figure, and their values are given below. Determine the fourth
order polynomial that best fits the data points. Make a plot of
the data points and the curve that corresponds to the polynomial.
Strain €
0 0.4 0.8 1.2 1.6 2.0 2.4
Stress (MPa) 0 3.0 4.5 5.8 5.9 5.8 6.2
Strain €
Stress (MPa)
2.8 3.2 3.6
7.4 9.6 15.6 20.7
4.0 4.4 4.8 5.2 5.6 6.0
26.7 31.1 35.6 39.3 41.5
36
Strain
192
(b) Write a program in a script file that plots the data points and the curve of the cubic polynomial that
best fits the data.
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