What are that iteration methods compare different iterative method?

What are that iteration methods compare different iterative method? What are that iteration methods compare different iterative method? What are the iteration methods? An iterative method is a powerful device of solving and finding the roots of the non linear equations. It is a process that uses successive approximations to obtain more accurate solutions to a linear system at each step. Such a method involves a large number of iterations of arithmetic operations to arrive at a solution for which the computers are very often used in its process to make the task simple and efficient. Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called iteration and the results of one iteration are used as the starting point for the next iteration. For example, to solve the quadratic equation we may choose any one of the following iteration methods: a0x^2 +a1x+a2=0 a) Xk+1 = -a2+a0xk^2/a1, k=0,1,2 b) Xk+1= -a2/a0xk+a1,k=0,1,2- Types of iteration methods: Based upon the number of initial approximation values iteration methods can be divided into two categories: Bracketing iteration methods Open end iteration methods Bracketing iteration method: These methods are also known as interpolation methods. Under these methods we start with two initial roots that in bracket, then systematically reduce the width of the bracket until the desired solution is arrived at. There are two popular methods under this category: Bisection method Regular_falsi method Open end iteration method: these methods are known as extrapolation methods. Under these methods we start with one or two initial roots that do not need the bracket the root. These methods are various types: Netwon_raphson method Secant method Mullers method Bisection, regular_falsi and netwon_raphson methods are under root finding algorithm. Root finding algo: A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f(x) = 0, for a given function f. Such an x is called a root of the function f. Iteration method is obtain the initial approximation to the root is based upon the intermediate value theorem. This theorem is states that: if f(x) is continuous function on some interval[a,b] and f(a).f(b)