Bisection
In numerical analysis, bisection is a root-finding algorithm which works by dividing an interval in half, and then selecting the interval in which the root exists.Given two starting points L and R which are guaranteed to bracket a root of function F, the bisection method divides the interval in two by doing M=(L+R)/2 and tries to find if a sign change occurs between L and M or between M and R. The bisection algorithm is then applied to the sub-interval where the sign change occurs, meaning that the bisection algorithm is inherently recursive.
It is numerically less efficient than Newton's method but it is much less prone to odd behavior.
Here is a representation of the bisection method in Visual Basic code. xR is the guess to the right of the root and xL is the guess to the right of the root. The initial xR and xL must be chosen so that f(xR) and f(xL) are opposite signs (they 'bracket' a root). Epsilon specifies how precise the results will be.
'Bisection Method
'Start loop
Do While (xR - xL) > epsilon
'Calculate midpoint of domain
xM = (xR + xL) / 2
'Find f(xM)
If ((f_of(xL, degT) * f_of(xM, degT)) > 0) Then
'Throw away left half
xL = xM
Else
'Throw away right half
xR = xM
End If
Loop
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?)