Newton's Method Convergence Plot

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Zyruss Edjan
Zyruss Edjan 2019-10-17
回答： Sid Singh 2019-10-21
Im currently trying to creat a convergence plot for my Newton's Method code. But I keep on getting a function error message that says Index exceeds the numbers of elements. I'm not really sure how to fix it.
function x_root = newtonze(x_est, tol, max_iter)
w = 20*10^3; L = 4; E = 70*10^9; I = 52.9*10^(-6);
for i = 1:max_iter
Xi = x_est - ((w*(7*L^4 - 30*L^2*x_est^2 + 15*x_est^4))/(360*E*I*L))/(-(w*x_est*(L^2 - x_est^2))/(6*E*I*L));
if abs((Xi-x_est)/x_est) < tol
x_root = Xi;
break
end
x_est=Xi;
end
x_root=x_est;
hold on
% Plot evolution of the solution
figure('Color','White')
plot(0:max_iter-1,x_root(1:max_iter),'o-')
title('Newton''s Method Solution: $f(x) = x + x^{\frac{4}{3}}$','FontSize',20,'Interpreter','latex')
xlabel('Iteration','FontSize',16)
ylabel('$x$','FontSize',16,'Interpreter','latex')
end

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回答（1 个）

Sid Singh
Sid Singh 2019-10-21
Hi, you are trying to plot a scalar value "x_root" against a time series which is why you are getting the error. Create an array
x_root = zeros(1, max_iter);
for i = 1:max_iter
Xi = x_est - ((w*(7*L^4 - 30*L^2*x_est^2 + 15*x_est^4))/(360*E*I*L))/(-(w*x_est*(L^2 - x_est^2))/(6*E*I*L));
if abs((Xi-x_est)/x_est) < tol
x_root(i) = Xi;
break
end
x_est=Xi;
end
and store values in that array. You would get zeros in the plot where this
if abs((Xi-x_est)/x_est) < tol
condition is not being met.

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