Termination Condition
In addition to a routine for reducing the size of the bracketing of the solution, a complete algorithm must have a termination condition. The one provided in the book Numerical Recipes in C is based on testing the gaps among, and, terminating when within the relative accuracy bounds:
where is a tolerance parameter of the algorithm and is the absolute value of . The check is based on the bracket size relative to its central value, because that relative error in is approximately proportional to the squared absolute error in in typical cases. For that same reason, the Numerical Recipes text recommends that where is the required absolute precision of .
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