Getting infinite looping and NaN error ( find the minimum of a function using Quadratic Approximation method )

Hey!

Im trying to find the minimum of the function using quadratic approximation method. But here Im getting NaN error in my matrices. I cannot find why. As well as there is something wrong with loop.

thanks.

clc

clear

f = @(x) exp((x.^4 + x.^2 -x + sqrt(5))./5) + sinh((x.^3 + 21.*x + 9)./(21.*x + 6)) -3 ;

%QUADRATIC APPROXIMATION METHOD

a = 0;

b = 1;

e = 0.01; % ε=0.0001 % ε=0,0000001 % ε=10^-17

x1=a; x2=(a+b)/2; x3=b;

figure; X = [a,b]; Y = [0,0];

plot(X,Y,'red','linewidth',8);

xlabel('intervals of uncertainty');

ylabel('iteration number');

title('ε = 0.01');

hold on;

grid on;

n = 0;

while (b-a>=e)

f1 = f(x1);

f2 = f(x2);

f3 = f(x3);

V = [x1^2,x1,1 ; x2^2,x2,1 ; x3^2,x3,1] ;

B = [f1 ; f2 ; f3] ;

P = linsolve(V,B) ;

xk = -P(2)/(2*P(1));

if xk>= x2

x1 = x2;

x2 = xk;

f1 = f2;

f2 = f(x2);

else

x3 = x2;

x2 = xk;

f3 = f2;

f2 = f(x2);

end

n=n+1;

X = [x1,x3]; Y = Y + n;

plot(X,Y,'red','linewidth',8);

end

xmin = (a+b)./2;

fprintf('The number of iterations = %d\n',n);

fprintf('Number of calculated values = %d\n',n+3);

fprintf('The point of minimum = %.4f\n',(xmin);

fprintf('Minimum of the function = %.4f\n',f((xmin)));

[Voss]

" ... there is something wrong with loop"

None of b, a, or e change inside the while loop, so if the while condition (b-a>=e) is true when the loop starts, it will be true forever and the loop will never stop.

[Janidu]

Do I need to change the while condition? I cannot figure it out.

[Voss]

Maybe it should be something like this?

while abs(x3-x1) >= e

[Janidu]

thank you! I will try!