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(6pts) Let us compare between different root-finding methods. You should answer

ID: 3702781 • Letter: #

Question

(6pts) Let us compare between different root-finding methods. You should answer the questions as clear as possible. Show concrete examples is helpful if your explanation is not precise enough. (a) Name a situation that the (FP) method of False Position (Regula Falsi) is better 2. (b) Name a situation that Newton's method is better than the Bisection method and (c) Name a situation that Newton's method is better than the Secant method and Bonus: Writing codes and show the convergence speed than the (B) Bisection method, also, a situation that (B) is better than (FP) vice versa vice versa

Explanation / Answer

A)Falsi position is better when we retain two points which certainly bracket a root and for fast process

bisection method is better when root lies in sub interval for further processing and it if of low cost and robust

B) Newton's method converges quadradically whereas bisection method converges linearly

situation in which Newton's method is better than Bisection method are

the process is to be fast , iteration are to be send to into blue yonder

situation in which Bisection method is better than Newton's method are

when the process is to be stable, and it should have convergence

C) secant method is better when

as the secant method is faster than Newton's method despite the slower convergence, because it only requires one new function evaluation for each iteration, while Newton's method requires two.and if we need a tangent but we don't know the derivative, it can be estimated

Newtons" method is betteer when we want the convergence to be speed and if we see the cost