4. Using the MATLAB command Uniform vs.Chebyshev Interp on the Math Linux networ

Question

4. Using the MATLAB command Uniform vs.Chebyshev Interp on the Math Linux network, report on the maximum absolute error in polynomial interpolation for the function f(x) = 1/(1 +r2) on the interval 5,5], for the equidistant (uniform, evenly spaced) nodes and the Chebyshev nodes, for n 5, 15, 25, 35, i.e., report on (4) Report on the value obtained with Chebyshev points for n-25. Which subdivision is best (equidistant or Chebyshev)? (4) )1.49 10-2, (2)1.441 102 (3)1.39 102, (4) 1.341 102, (5) 1.292, (6124 0-2, (7) 1.191 102, (8) 1.141 02, (9) .091 102, (10 1.04 102

Explanation / Answer

function [] = lagranges_interpolation ()
a=[5,10,20];
error=[];
for i=a
error=[error,lagranges(i,-5,5)];
end
plot(a,error);
end

function [error]=lagranges(N,x1,x2)
i=x2-x1/N;
a=x1:i:x2;
dim=size(a);
y=(1)./(1+a.^2);
approx=zeros(1,dim(2));
k=0;
for i=1:dim(2)
approx(i)=ind_lag(a,a(i));
end
  
error=sqrt(sum((approx-y).^2))/dim(2);
end

function [approx]=ind_lag(a,x)
sum=0;
for i=1:size(a)
mult=1;
for j=1:size(a)
if(i!=j)
buf=(x-a(j))/(a(i)-a(j));
mult=mult*buf;
end

end
sum=sum+mult;
end
approx=sum;
end

%yes the approximation gets better with increase in number of points

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