Question

Please help me solve this. #4 a&b. thanks

eilymai retine, or you m yur ova rodinT ur pl nda listing of your code. (b) Repeat part (a) with a polynomial of degree 12 that interpolates f at 13 scaled Chebyshev points, x 5 cos 12 Again you may use MATLAB's polyfit and polyval routines to fit the polyno- mial to the function at these points and evaluate the result at points throughout the interval, or you may use the barycentric interpolation formula (8.6) with weights defined by (8.5) or (8.16) to evaluate the interpolation polynomial at points other than the interpolation points in the interval [-5, 5]. Turn in your plot and a listing of your code.

Answer 1

Matlab code for answering question 4a. and 4b. clear all close all %function for which interpolation have to do 13 equally spaced points between -5 to 5 xx I-5:5/6:5] yy-f (xx)i %12th degree polynomial coefficients p- polyfit(xx , yy, 12); polyval code xl -linspace(-5,5,1001); y1 = polyval (p,x1); figure(1) plot (xx, yy, ro hold on plot (x1,yl,'linewidth',2) hold off title( Plotting for Runge function equally spaced point' xlabel ( ' x' ) ylabel(f(x)') legend('Actual data", polynomial fit') 813 Chebyshev points between -5 to 5 for j= 1:13 xx (j)-5*cos (pi*(j-1)/12); end 12th degree polynomial coefficients p-polyfit (xx,yy, 12); epolyval code xl - linspace(-5,5,1001) yl - polyval (p, xl); figure (2) plot (xx, yy, 'ro) hold on plot (xl,yl, 'linewidth',2) hold off title 'Plotting for Runge function Chebyshev points) xlabel (·x' ) ylabel('f(x) legend('Actual data, 'polynomial fit') 응88888888888888888888 End of Code 888888888888888888옹

Plotting for Runge function equally spaced point O Actual data 3-1 -2 Plotting for Runge function Chebyshev points O Actual data 0.9 0.B 0.7 0.6 0.5 04 0.3 0.2 0.1

%%Matlab code for answering question 4a. and 4b.
clear all
close all
%function for which interpolation have to do
f=@(x) 1./(1+x.^2);

%13 equally spaced points between -5 to 5
xx=[-5:5/6:5];
yy=f(xx);
%12th degree polynomial coefficients
p = polyfit(xx,yy,12);

%polyval code
x1 = linspace(-5,5,1001);
y1 = polyval(p,x1);
figure(1)
plot(xx,yy,'ro')
hold on
plot(x1,y1,'linewidth',2)
hold off

title('Plotting for Runge function equally spaced point')
xlabel('x')
ylabel('f(x)')
legend('Actual data','polynomial fit')

%13 Chebyshev points between -5 to 5
for j=1:13
  
    xx(j)=5*cos(pi*(j-1)/12);
  
end
yy=f(xx);
%12th degree polynomial coefficients
p = polyfit(xx,yy,12);

%polyval code
x1 = linspace(-5,5,1001);
y1 = polyval(p,x1);
figure(2)
plot(xx,yy,'ro')
hold on
plot(x1,y1,'linewidth',2)
hold off

title('Plotting for Runge function Chebyshev points')
xlabel('x')
ylabel('f(x)')
legend('Actual data','polynomial fit')

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