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
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