Newton-Raphson method

From Programming In C

Exercise 4.2

Note: this is an example of an actual assessment

The Newton-Raphson Method is a powerful method of finding the roots of the function f(x), that is the values of x for which f(x) = 0. Suppose that x_old is an estimate of the root. Then a better estimate is x_new which is defined by:

where g(x) = df(x)/dx.

This procedure is iterated until convergence is achieved, defined by |x_new – x_old| < acc, where acc is a user-defined accuracy.

Use the Newton-Raphson method to find the root of the function f(x) = exp(-x) – x, starting the iteration at x = -10.0.

Use a do-while loop (or equivalent) algorithm.

How many iterations are required to obtain an accuracy (acc) of 10^-6, and what is the solution at this accuracy ?

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