Derive an interval subdivision method, similar to bisection, that is a first-order method with C =...

Transcribed Image Text:

Derive an interval subdivision method, similar to bisection, that is a first-order method with C = 1/3. Suppose that the stopping condition for the secant method is ((x k-x_{k-1})/x k < tol. Why should you not take tol = 10^{-20}? What if you use the bisection method (instead of secant)? Derive an interval subdivision method, similar to bisection, that is a first-order method with C = 1/3. Suppose that the stopping condition for the secant method is ((x k-x_{k-1})/x k < tol. Why should you not take tol = 10^{-20}? What if you use the bisection method (instead of secant)?