(a) What are the four important factors for deciding whether an iterative method for finding solution to the nonlinear equation is good or not? (b) The bisection method converges linearly to the solution x ? at a rate of 1/2. |x ? ? xn| ? b ? a 2 n Consider the function f(x) = x 2 ? 2 on the interval [1, 2]. Estimate the minimum number of iterations necessary to guarantee the approximation to ? 2 using the bisection method is within of the actual value |x ? ? xn| ? for = 10?3 .

(a) What are the four important factors for deciding Whether an iterative method for nding solution to the nonlinear equation is good or not? (b) The bisection method converges linearly to the solution 33* at a rate of 1/2. b a. 2n Consider the function f (1') = 3:2 2 on the interval [1,2]. Estimate the minimum number of iterations necessary to guarantee the approximation to using the bisection method is within 6 of the actual value |a:* x| 5 6 for e = 103. lat\" xn| S