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
Soccer in the United States effectively the amateur fifth division of soccer in the United States. The Lamar Hunt U.S. Open Cup is a knockout tournament in American soccer. The tournament is the oldest ongoing national soccer competition in the U.S. and was historically open to all United States Soccer Federation affiliated teams, from amateur adult club teams to the professional clubs of Major League Soccer. Since the 2016 edition, professional teams that are majority-owned, or whose playing staff is managed, by a higher-division outdoor professional team have been barred from the competition; all other U.S. Soccer-affiliated teams remain eligible to enter. The Open Cup