Error - matrix dimensions must agree

Hi i cant seem to work out why this error keeps appearing in my code. thanks

x0 = 2;

y0 = 2;

x = [x0; y0];

iter = 0;

max_iter = 100;

tol = 0.1;

err = norm(f(x));

while iter <= max_iter && err >= tol

iter =iter + 1;

x = x - Jacob(x)\f(x);

err = norm(f(x));

end

function y = f(x)

y = (9-x.^2).^0.5;

f(x) = x.^2+y.^2-9;

g(x) = x.^2.*y+y.^3+1;

y = [f(x); g(x)];

end

function y = Jacob(x)

y = (9-x.^2).^0.5;

dfdx(x) = 2.*x;

dfdy(x) = 2.*y;

dgdx(x) = 2.*x.*y;

dgdy(x) = x.^2+3.*y.^2;

y = [dfdx(x) ,dfdy(x); dgdx(x) ,dgdy(x)];

end

[Joe Wheeler]

apologies, the error is found here:

Error in systems_of_nonlinear_equations (line 14)

x = x - Jacob(x)\f(x);

Answer 1

[Mischa Kim]

Hi Joe, I think this is what you are trying to do:

x0 = 2;
y0 = 2;
x = [x0; y0];
iter = 0; 
max_iter = 100; 
tol = 0.001; 
err = norm(f(x));
 
while iter <= max_iter && err >= tol
    iter = iter + 1;
    x    = x - Jacob(x)\f(x);
    err  = norm(f(x));
end
 
function Y = f(X)
x = X(1); y = X(2);
f = x.^2+y.^2-9;
g = x.^2.*y+y.^3+1;
Y = [f; g];
end
 
function Y = Jacob(X)
x    = X(1); y = X(2);
dfdx = 2.*x;
dfdy = 2.*y;
dgdx = 2.*x.*y;
dgdy = x.^2+3.*y.^2;
Y    = [dfdx ,dfdy; dgdx,dgdy];
end

I will let you work through the code.