hey!! i am stuck here. i am new. help please.

my task is to do this:

i have wrote the codde as:

clc

clear all

xdata=linspace(-1,1,9);

ydata=1./(1+14*xdata.^2);

x=linspace(-1,1,1000);

y=lagrangeInterp(xdata,ydata,x);

plot(x,y,'b',xdata,ydata,'*r');

function [yhat]=lagrangeInterp(x,y,interpx)

X=x;

f=y;

x=interpx;

l=0;

for i=1:length(X)

li=1;

for j=1:length(X)

if i~=j

li=(li).*((x-X(j))/(X(i)-X(j)));

end

end

l=(l)+((li)*f(i));

end

yhat=l;

end

Can you tell me what will happen if we use nodes that are not equispaced in x. Instead,

use the Chebyshev nodes {xk}given by

xk = -cos(pi * k/n); k = 0, 1, ..... ,n

Answer 1

[Andy]

You do not say why this is wrong, the code runs. Is there an issue with the number of nodes and the linspace. The question says use n=9 (i.e. 10 nodes) but using xdata=linspace(-1,1,9); only generates 9 nodes. If you change to

xdata=linspace(-1,1,10);

This gives 10 nodes and perhaps the answer you are looking for.

[rana zain]

i get it. but i want to find the plots mentioned in part (ii) named as plots of "interpolant vs x" ,original function vs x, and the set. i am unable to get answers for that.

[Andy]

This adds some data for the original function and adds it to the plot. Just insert/replace into your code.

xdata1=linspace(-1,1,200);
ydata1=1./(1+14*xdata1.^2);

plot(x,y,'b',xdata1,ydata1,'g',xdata,ydata,'*r');

[rana zain]

got it!!

can you tell me what will happen if we use nodes that are not equispaced in x. Instead,

use the Chebyshev nodes {xk}given by

xk = -cos(pi * k/n); k = 0, 1, ..... ,n

[Andy]

Sorry, I can't help with that, I'm not familiar with use of the interpolation functions.

[rana zain]

Can you tag someone who can?/