Question

Please solve using matlab and post the code used

1) Consider the following input data: x = [O 3.6 10 12 16.4 18.4 24]; y = [52 32.830 6.670 7 5.030 2*pi 8]; Use polyfit to a) determine the best polynomial fit for desired order n (1, 2, 3, 4, 5) b) determine the error between fitted and experimental data for the values of x c) determine the time to compute order range 0 to 6 using tic toc d) Bonus: compare the computational time versus polyfit order n (1, 2, 3, 4, 5).

Answer 1

$$Matlab code for polyfit and polyval clear all close all $input data x=[0 3.6 10 12 16.4 18.4 24]; y=[52 32.83 6.67 7 5.03 2*pi 8]; $desired order n=[1 2 3 4 5); for i=1:5 tic p=polyfit(x,y,n(i)); p_val=polyval(P,x); tt(i)=toc; err=norm(P_val-Y); fprintf('For n=&d error norm=3f\n',i,err) fprintf('\tComputational time = $f\n', tt(i)) end plot in, tt) xlabel('order (n)) ylabel('computational time (t)') title('computational time vs. order number plot') 888888888888888 End of Code %%%%%%%%%% For n=1 error norm=25.492846 Computational time = 0.045948 For n=2 error norm=6.512056 Computational time = 0.005959 For n=3 error norm=3.885876 Computational time = 0.0049 74 For n=4 error norm=2.512141 Computational time = 0.011746 For n=5 error norm=1.852285 Computational time - 0.015512

computational time vs. order number plot computational time (1) di 15 2 2.5 3 order (n) 3.5 4 4.5 Published with MATLAB® R2018a

%%Matlab code for polyfit and polyval
clear all
close all

%input data
x=[0 3.6 10 12 16.4 18.4 24];
y=[52 32.83 6.67 7 5.03 2*pi 8];

%desired order
n=[1 2 3 4 5];
for i=1:5
  
    tic
    p=polyfit(x,y,n(i));
    p_val=polyval(p,x);
    tt(i)=toc;
    err=norm(p_val-y);
    fprintf('For n=%d error norm=%f\n',i,err)
    fprintf('\tComputational time = %f\n',tt(i))
  
end
  
plot(n,tt)
xlabel('order (n)')
ylabel('computational time (t)')
title('computational time vs. order number plot')

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