emth 271 lab 3

newton_function.m

function results = mymultinewtfunction(x, func, niter, tol)

for i = 1:niter
    n = max(size(x));
    
    %f = [(log(x(1)) - x(2)) , ((x(1)^2+2*x(1)-24)/25 - x(2))];
    %J = [1/x(1), -1 ; 2*x(1)/25+2/25 , -1];
    f = func(x);
    J = zeros(n);
    
    for k = 1:n
        for l = 1:n
            e = zeros(n,1);
            e(l) = 1;
            h = 1e-8;
            pd = (func(x+h*e) - func(x))/h;
            J(k,l) = pd(k);
        end
    end
    
    deltax = J\-f';
    xnew = x + deltax;

    relativeError = norm(xnew - x,Inf)/norm(xnew,Inf);
    if relativeError <= tol
        break
    end

    verbose = 0;
    if verbose && i < 6
       f
       J
       xnew
       relativeError
    end
    
    x = xnew;
    
    if i == niter
       results = 1;
       fprintf('\nmax iterations reached\n\n')
       return
    end
    
end

fprintf('\ninterations = %i\n\n',i)
results = x;
end