False position method As a result, unlike the bisection method, the width of the bracket does not tend to zero (unless the zero is at an inflection point around which ). As a consequence, the linear approximation to , which is used to pick the false position, does not improve as rapidly as possible. One example of this phenomenon is the function on the initial bracket [−1,1]. The left end, −1, is never replaced (it does not change at first and after the first three iterations, is negative on the interval) and thus the width of the bracket never falls below 1. Hence,
Captain of the guard Captain of the guard The Captain of the Guard is a position for a military force. It is also a position for jail and prison terms. A Captain of the Guard is the commanding position of a military security force. The position of Captain of the Guard is not or no longer associated with the rank of Captain. The Guard is commonly associated with bodyguard duty for royalty or head of state, but the Guard can refer to the military security force of a city or region such as a province, state, or territory. A captain of the guard is