Editing Root-finding algorithm (section)

=== Bisection method ===
The simplest root-finding algorithm is the [[bisection method]]. Let {{math|''f''}} be a [[continuous function]] for which one knows an interval {{math|[''a'', ''b'']}} such that  {{math|''f''(''a'')}} and {{math|''f''(''b'')}} have opposite signs (a bracket). Let {{math|1=''c'' = (''a'' + ''b'')/2}} be the middle of the interval (the midpoint or the point that bisects the interval). Then either {{math|''f''(''a'')}} and {{math|''f''(''c'')}}, or {{math|''f''(''c'')}} and {{math|''f''(''b'')}} have opposite signs, and one has divided by two the size of the interval. Although the bisection method is robust, it gains one and only one [[bit]] of accuracy with each iteration. Therefore, the number of function evaluations required for finding an ''ε''-approximate root is <math>\log_2\frac{b-a}{\varepsilon}</math>. Other methods, under appropriate conditions, can gain accuracy faster.