Syntax error which I cannot find ( find the minimum of a function using Quadratic Approximation Method )

Hey there!

Im trying to find the minimum of a function using quadratic method and I'm getting some errors which I cannot find.

And maybe there are mistakes in my code also. Hope your help to find out my mistakes.

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;
x1=a; x2=0.5; x3=b; 

line=x3 - x1; 
figure; X = [a,b]; Y = [0,0]; 
plot(X,Y,'black','linewidth',4); 
hold on; 
grid on; 
n = 0;

while (line>e) 
    n=n+1; 
    f1 = f(x1); 
    f2 = f(x2); 
    f3 = f(x3);
p = ( f1*(x2.^2-x3.^2) + f2*(x3.^2-x1.^2) + f3*(x1.^2x2.^2) ) / (2*(f1*(x2-x3)+f2*(x3-x1)+f3*(x1-x2)));

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON

if p >= x2 
    x1 = x2; 
    x2 = p;
else 
    x3 = x2; 
    x2 = p; 
end

fprintf('------%.10f\n',x1,x2,x3); 
line = x3-x1; 
fprintf('line=%.10f\n',line); 
X = [x1,x3]; Y = Y +n; 
plot(X,Y,'black','linewidth',4);

end 
fprintf('The number of iterations is %d\n',n);
fprintf('Number of calculated values is %d\n',n+3); 
fprintf('The point of minimum is %.4f\n',(x1+x3)/2); 
fprintf('Minimum is %.4f\n',f((x1+x3)/2));

Answer 1

[Walter Roberson]

p = ( f1*(x2.^2-x3.^2) + f2*(x3.^2-x1.^2) + f3*(x1.^2x2.^2) ) / (2*(f1*(x2-x3)+f2*(x3-x1)+f3*(x1-x2)));
                                                ^^^^^^^^^^

Taking something ^2x2 is not valid syntax. Looking at the other clauses you probably forgot a - and wanted x1.^2-x2.^2

[Janidu]

ohh thanks!