function quadraticinterpolation(F,x1,x2,x3,e)
%x1<x2<x3
f1=polyval(F,x1);
f2=polyval(F,x2);
f3=polyval(F,x3);
if ((f1<=f2)|(f3<=f2))
disp('error')
return
end
%x_initial=0.5*((x2^2-x3^2)*f1+(x3^2-x1^2)*f2+(x1^2-x2^2)*f3)/((x2-x3)*f1+(x3-x1)*f2+(x1-x2)*f3);
c1=(f3-f1)/(x3-x1);
c2=((f2-f1)/(x2-x1)-c1)/(x2-x3);
x_initial=0.5*(x1+x3-c1/c2);
x_temp=x_initial;
f_temp=polyval(F,x_temp);
while abs(f_temp-f2)>e
%x_temp=0.5*((x2^2-x3^2)*f1+(x3^2-x1^2)*f2+(x1^2-x2^2)*f3)/((x2-x3)*f1+(x3-x1)*f2+(x1-x2)*f3);
c1=(f3-f1)/(x3-x1);
c2=((f2-f1)/(x2-x1)-c1)/(x2-x3);
x_temp=0.5*(x1+x3-c1/c2);
f_temp=polyval(F,x_temp);
if f_temp<f2
x3=x2;
f3=f2;
x2=x_temp;
f2=f_temp;
elseif f2<f_temp
x1=x_temp;
f1=f_temp;
else
x=x_temp;
f=f_temp;
return
end
end
x=x2
f=f2
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