Hi,
It seems that your output tolerance is not under the specified "tolX". To improve this, you can use a "norm" (like the Euclidean norm) function to get a single value representing the "distance" between your old and new "x" values and then compare this against your tolerance. Currently, the tolerance check is performed against the vector "err(:,i)" having absolute error calculation directly; instead of it, update the error using the "norm" of "deltaX" Refer to the modified code:
x0 = [3; -1.5];
maxIter = 50;
tolX = 1e-14;
x = x0;
xold = x0;
format long
xv = nan(maxIter,1);
yv = xv;
err = zeros(1, maxIter); % Initialize the error array
for i = 1:maxIter
[f,j] = newtraph(x);
deltaX = j\f; % Calculate the change in x
x = x - deltaX; % Update x
err(i) = norm(deltaX); % Update the error using the norm of deltaX
if err(i) < tolX
break;
end
xv(i) = x(1); % Store the x and y values
yv(i) = x(2);
end
% Remove NaN values from xv and yv
xv = xv(~isnan(xv));
yv = yv(~isnan(yv));
OutputValues = table(xv, yv, 'VariableNames',{'X','Y'})
display(x)
fprintf('Number of iterations: %d \n',i)
fprintf('Final tolerance before accepted tolerance: %d \n' ,err(i)) % Adjusted the print format to show more precision
function [fval,jac] = newtraph(X)
x = X(1);
y = X(2);
fval(1,1)=x+exp(-x)+y^3;
fval(2,1)=x^2+2*x*y-y^2+tand(x);
jac = [1-exp(-x), 3*y^2;
2*x+2*y+1+(tand(x))^2, 2*x-2*y];
end
This resulted in the error of "3.722328e-15", which is less than your defined tolerance. For more information on the "norm" function, refer to the below documentation:
