It is numerically less efficient than Newton's method but it is much less prone to odd behavior.
In geometry, bisection refers to dividing an object exactly in half, usually by a line, which is then called a bisector. The most often considered types of bisectors are segment bisectors and angle bisectors.
A segment bisector passes through the midpoint of the segment. Particularly important is the perpendicular bisector of a segment, which, according to its name, meets the segment at right angles. The perpendicular bisector of a segment also has the property that each of its points is equidistant from the segment's endpoints.
An angle bisector divides the angle into two equal angles. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle.
(Please add figures to this entry. Should ruler-and-compass constructions be included?)