In the Newton method for finding a root r of f (x) = 0, we start with x0 and compute the...
In the Newton method for finding a root r of f (x) = 0, we start with x0 and compute the sequence x1, x2, . . . using the formula xn+1 = xn − f (xn)/ f ′(xn). To avoid computing the derivative at each step, it has been proposed to replace f ′(xn) with f (x0) in all steps. It has also been suggested that the derivative in Newton’s formula be computed only every other step. This method is given by
Numerically compare both proposed methods to Newton’s method for several simple functions that have known roots. Print the error of each method on every iteration to monitor the convergence. How well do the proposed methods work?
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