What are that iteration methods compare different iterative method?

What are that cringle orders compare unalike iterative method?What are that looping methods compare different iterative method?What are the loop 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 musical themes to obtain more accurate solutions to a linear system at all(prenominal) 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 assign 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 too called iteration and the results of one iteration are used as the starting point for the next iteration.For example, to crystalise the quadratic equation we may choose any one of the following iteration methods a0x2 +a1x+a2=0 a) Xk+1 = -a2+a0xk 2/a1, k=0,1,2b) Xk+1= -a2/a0xk+a1,k=0,1,2-Types of iteration methodsBased upon the number of initial approximation set iteration methods can be divided into two categories Bracketing iteration methods Open end iteration methodsBracketing iteration methodThese 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. in that respect are two popular methods under this category Bisection method Regular_falsi methodOpen 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 methodBisection, regular_falsi and netwon_raphson methods are under root finding algorithm.Root finding algoA root-finding algorithm is a numerical method, or algorithm, for fin ding a value x such that f(x) = 0, for a given extend 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 intervala,b and f(a).f(b)