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
Midfielder Midfielder A midfielder is an association football position. Midfielders are generally positioned on the field between their team's defenders and forwards. Some midfielders play a disciplined defensive role, breaking up attacks, and are otherwise known as defensive midfielders. Others blur the boundaries, being more mobile and efficient in passing: they are commonly referred to as deep-lying midfielders, play-makers, box-to-box, or holding midfielders. The number of midfielders on a team and their assigned roles depends on the team's formation; the collective group of these players on the field is sometimes referred to as the midfield. Most managers assign at least one