Answer this Newtons Method problem

[James Tursa]

What have you done so far? What specific problems are you having with your code?

Answer 1

[Wan Ji]

why not use fsolve or fzero? The following is newton's method

function main
f = @(x) [
    sin(x(1)*x(2)) + x(1) - x(2);
    x(2)*cos(x(1)*x(2)) + 1;
    ];
TOL = 1e-3;
err = 1;
x0 = [1;2];
iter = 0;
fprintf('Iteration\tx1\tx2\tf1(x1,x2)\tf2(x1,x2)\n');
while err>TOL
    iter = iter + 1;
    x1 = x0 - diffmat(f,x0,1e-3)\f(x0) ;
    err = norm(x1-x0);
    x0 = x1;
    fval = f(x1);
    fprintf('%d\t%f\t%f\t%f\t%f\t\n', iter, x1(1), x1(2), fval(1), fval(2));
end
end
function m = diffmat(fun, x, h) 
f0 = fun(x);
m = zeros(numel(f0), numel(x));
for i = 1:1:numel(x)
    x0 = x;
    x0(i) = x0(i) + h;
    fi = (fun(x0) - f0)/h;
    m(:,i) = fi;
end
end

Result printed:

Iteration	x1	x2	f1(x1,x2)	f2(x1,x2)
1	1.079754	1.945311	-0.002579	0.017148	
2	1.086147	1.943707	-0.000034	0.000076	
3	1.086187	1.943685	0.000000	-0.000000