matlab 29.03.2018

%ce s-a lucrat inainte
function a=METNAIVA(X,Y)
    n=length(X)-1
    for i=1:n+1
        for j=1:n+1
            A(i,j)=X(i)^(j-1)
        end
    end
    for i=1:n+1
        Ai=A
        Ai(:,i)=Y(:)
        a(i)=det(Ai)/det(A)
    end
end



function lab3
 syms x;
 f(x)=exp(2*x);
 n=3;
 X=linspace(-1,1,n+1)
 Y=f(X)
 ezplot(f,[-1,1])
 hold on
 plot(X,Y,'r+');
 a=METNAIVA(X,Y)
 Pn=0
 for i=1:n+1
     Pn=Pn+(x^(i-1))*a(i);
 end
 ezplot(Pn,[-1,1])
 Pn=inline(Pn,'x')
 Pn(0.1)
end

function y=METL(X,Y,x)
n=length(X)-1;
Pn=0;
for k=1:n+1
    L=1;
    for j=1:n+1
        if (j~=k)
            L=L*(x-X(j))/(X(k)-X(j));
        end
    end
    Pn=Pn+L*Y(k);
end
y=Pn;
end


function lab3b
syms z;
 f(z)=exp(2*z);
 n=3;
 X=linspace(-1,1,n+1);
 Y=f(X);
 x=linspace(-1,1,1000);
 for i=1:length(x)
     y(i)=METL(X,Y,x(i));
 end
 plot(X,Y,'r+')
 plot(x,y)
end

%ce am lucrat eu