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

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Janidu
Janidu 2022-11-10
评论： Janidu 2022-11-10
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)));
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