For the nonlinear equation f (x) = x2 − x − 2 = 0 with roots 1 and 2, write four fixed-point problems x = g(x) that are equivalent. Plot all of these, and show that they all intersect the line x = y. Also, plot the convergence steps of each of these fixed-point iterations for different starting values x(0). Show that the behavior of these fixed-point schemes can vary wildly: slow convergence, fast convergence, and divergence.
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