Question

please make sure the answer is correct %100

P1 This project requires you to solve the following problems. Some problems may require the use of a computer. It will be indicated where this is required. The following data point have been recorded for a particular experiment: (1,2), (2,5), (3,9), (4,12), (5, 21), (6,35). Set up the linear system that will enable you to compute the coefficients of the poly- nomial. To solve the system please use an algorithm and associated code to solve. It is recommended that Python be used however other languages will be accepted with prior email approval. Please note that for part b provide the following: 1. Your python code as a txt file which can be copy-pasted into the compiler 2. All variable definitions explaining clearly what they are used for 3. Output to be expected should clearly have wording indicating the solution.

Answer 1

• There are 6 data points given. We can fit a 5th degree polynomial on the points. This polynomial will have 6 coefficients.
• The 6 coefficients can be obtained with numpy's polyfit method.

program logic:

• Define the data points x and y as vectors.
• pass the vectors to polyfit() function and obtain the coefficients in an array p.
• plot the x,y datapoints and the fit to check the approximation.

program:

Note: documentaion of the code is provided in comments

import numpy as np
import matplotlib.pyplot as plt

x = [1,2,3,4,5,6]
y = [2,5,9,12,21,35]

#there are 6 data points
#it is possible to fit a 5th degree polynomial
#the fit will produce the coefficients as output

p = np.polyfit(x,y,5)
#x[0]**n * p[0] + ... + x[0] * p[3] + p[4] = y[0]
#x[1]**n * p[0] + ... + x[1] * p[3] + p[4] = y[1]
#...
#x[5]**n * p[0] + ... + x[5] * p[3] + p[4] = y[5]

xfit = np.linspace(1,6,100)
yfit = np.polyval(p,xfit)

plt.scatter(x,y,label="data points")
plt.plot(xfit,yfit,label="fit")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()
plt.show()

output plot:

- 中Q主 19 35 fit data points 30 25 20 15 10 5 3 4 5 N х