Higher-order convergence algorithm for reciprocal and square root Takayuki HOSODA Nov. 16, 2009 The Newton-Raphson method is a first-order approximation of a function f(x) around the approximate value of xn . Its convergence speed can be increased by higher order approximation. Japanese edition is here. Reciprocal The recurrence formula for reciprocal 1 / A by Newton-Raphson method is Given by Xn+