![]() This tangent will have the equation as y= f´(x 0)(x - x 0) + f(x 0). We draw a tangent line to the graph of function f(x) at point x = x 0. We can see graphically how Newton's Method works as follow: Newton Raphson Method. So we continue in this way, If x n is the current estimate, then the next estimate x n+1 is given by : The next estimate x 2 is obtained from x 1 in exactly the same way as x 1 was obtained from x 0: Now we put x 1 = x 0 + h, where x 1 is our new improved estimate, and we get the following equation Since h = r - x 0 is small we can use tangent line approximation as follow:Ġ = f(r) = f(x 0 + h) ≈ f(x 0) + hf´(x 0)Īnd unless hf´(x 0) is close to zero we have, The number h measures how far is x 0 is from true root. Theoryįor a continous and differentiable function f(x), let x 0 be a good approximation for root r and let r = x 0 + h. It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it. Newton's Method, also known as Newton-Raphson method, named after Isaac Newton and Joseph Raphson, is a popular iterative method to find a good approximation for the root of a real-valued function f(x) = 0. ![]() Reading time: 35 minutes | Coding time: 10 minutes
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