Is anything wrong with Eval function? I get value of pn =1 for all x values.

function HW_4_8()
    y= @(x)(1/(1+25*x.^2));
    %x=linspace(-1,1,41);
    for i=0:5
        x=cos(i*pi/40);
    end
    fprintf('Coefficient of the newton interpolation\n\n');
    a= Coef(x,y);
    for i=1:length(a)
        fprintf('%5.0f\t%15.10f\n',i-1,a(i));
    end
    xp=linspace(-1,1,200);
    fprintf('Approximate value of y(x)\n');
    fprintf('    n           x           p(x)');
    fprintf( '          y(x)              diff\n');
    for i=1:length(xp)
        p=xp(i);
        funval=(1./(1+25*p.^2));
        %  fplot(funval,[-1,1]);
        pn= Eval(x,a,p);
        D=abs(funval-pn);
        % disp(D);
        % fplot(diff,[-1,1]);
        fprintf('%5.0f\t%5.10f\t%15.10f\t%15.10f\t%15.10f\n',i,p,pn,funval,D);
    end
    %fplot(D,[-1,1]);
end
function[a]=Coef(x,y)
    mx=length(x);
    my=length(y);
    % if mx ~= my
    %     error('must be same lenght');
    % end
    T=zeros(mx,mx);
    T(:,1)=(my)';
    for j=2:mx
        for i=1:(mx-j+1)
            T(i,j)=(T(i+1,j-1)-T(i,j-1))/(x(i+j-1)-x(i));
        end
    end
    a=T(1,:);
end
function pn=Eval(x,a,p)
    m=length(a);
    sum=0;
    for i=1:m
        temo=1;
        for j=1:i-1
            temo=temo*(p-x(j));
        end
        sum =sum+a(i)*temo;
    end
    pn=sum;
end

[Are Mjaavatten]

x is not initialized to a vector, as you intend, but to a scalar. Try:

      x = zeros(6,1);
      for i=0:5
          x(i+1)=cos(i*pi/40);
      end

Furthermore your y function should use element-wise division:

y= @(x)(1./(1+25*x.^2));

And you should pass the value, not the function, to Coef:

a= Coef(x,y(x));

A more general advice is to split and conquer: Test and debug the subfunctions first. Make sure that they do what you want them to do before incorporating them in the main function.

I also think that you could benefit from a better understanding of Matlab. Take a look at this page . Or search the net for "Matlab tutorial" or Matlab introduction"

[Guillaume]

@Are, this would have been better as an answer (which we could have voted for)

[Muhtasim Ahmed]

Thanks @Are

[Are Mjaavatten]

Thanks for the feedbacks from both of you.

Guillaume: This started out as a brief comment on the x vector, but it sort of grew as I wrote. I should have considered changing it to it an answer.