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-Fundamentals: Numerical methods

3.2 Half interval method

This algorithm is generally used when an analytical expression for the derivative of the function f(x) = 0 with respect to the x is not available.

In this case the algorithm is as follows:

  1. Choose 2 values for x in such a way that it is: f(a) f(b) < 0

  2. Calculate the new value for xnew = [a + b]/2

  3. Calculate the new value for f(xnew)

  4. If f(xnew) is already almost zero (<e), xnew is the searched root

  5. If f(xnew) is >e, the procedure must be iterated from point 1 again until convergence. Of course, one of the new two values to choose in point 1 is xnew

Here below a scheme of the algorithm.

algorithm for root finding