False position method those relatively unusual unfavorable situations. The failure mode is easy to detect (the same end-point is retained twice in a row) and easily remedied by next picking a modified false position, such as or down-weighting one of the endpoint values to force the next to occur on that side of the function. The factor of 2 above looks arbitrary, but it guarantees superlinear convergence (asymptotically, the algorithm will perform two regular steps after any modified step, and has order of convergence 1.442). There are other ways to pick the rescaling which give even better superlinear convergence rates. The above adjustment
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