TEAM PROJECT. Method of False Position (Regula falsi).

Chapter 19, Problem 19.2

(choose chapter or problem)

TEAM PROJECT. Method of False Position (Regula falsi). Figure 427 shows the idea. We assume that f is continuous. We compute the x-intercept Co of the line through (ao, f(ao), (bo, f(bo. If f(co) = 0, we are done. If f(ao)f(c o) < 0 (as in Fig. 427), we set a 1 = ao, b 1 = Co and repeat to get Cl, etc. If f(ao)ffco) > 0, then f(co)f(b o) < 0 and we set al = Co, b 1 = bo, etc. (a) Algorithm. Show that Co = aof(bo) - bof(ao) f(bo) - f(ao) and write an algorithm for the method. (b) Comparison. Solve x 3 = 5x + 6 by Newton's method, the secant method, and the method of false position. Compare. (C) Solve X4 = 2, cos x = V~, and x + In x 2 by [he method of false position.