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
History of soccer in the United States 1924 when USFA created the National Amateur Cup. That spelled the death knell for the American Cup. It played its last season in 1924. Towards the end of the 1920s, a period in American soccer known as the "American Soccer Wars" ignited. The Soccer Wars regarded the internal conflicts with the American Soccer League and their affiliated clubs participating in the National Challenge Cup. The debate involved whether the United States Football Association or the American Soccer League was the true chief organization of American soccer at the time, and consequently wrecked the reputation and possibly even the popularity of