Question

solve any non-linear equation using Secant and Regula Falsi Methods. which method converges fast.? ​

Answer 1

Answer:

In the case of the secant method, both y and z approach the root, leading to log|x−y| growing similarly to that of the Fibonacci sequence, which can be solved to give an order of convergence of φ=(1+√5)/2, the golden ratio.

.

Newton's method can not always guarantee that condition. When the condition is satisfied, Newton's method converges, and it also converges faster than almost any other alternative iteration scheme based on other methods of coverting the original f(x) to a function with a fixed point.