False position method to "regula falsi" is sometimes called the Illinois algorithm. Ford (1995) summarizes and analyzes this and other similar superlinear variants of the method of false position. Put simply: When the new -value (that is, )) has the same sign as the previous one ()), meaning that the end point of the previous step will be retained, the Illinois version halves the -value of the retained end point in the next estimate computation. Suppose that in the -th iteration the bracketing interval is and that the functional value of the new calculated estimate has the same sign as . In this
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