# Newton's method

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Simple utility that finds solutions to equations using Newton's Method. To use, enter in an equation and an initial guess. Just like magic, the program will find a solution closest to your original guess.

Newton's method (http://en.wikipedia.org/wiki/Newton%27s_method) is a method of finding converging approximations of the roots of an equation. It is done by choosing an arbitrary guess x for the root, then using the x-intercept of the line tangent to the point (x, f(x)), using the derivative, as a closer root guess. This iteration is repeated until the root has been sufficiently approximated. In many cases, convergence to the root is at least quadratic (very quick) depending on the initial guess. If the initial guess lies on a vertex or critical point, the derivative will be zero and Newton's method will fail. Newton's method can be used to solve many equations by setting one side of the equation equal to zero and then applying the method. Interestingly, Joseph Raphson published this method first, and his method is the one that is taught most widely.

From Wikipedia: an initial guess xn is used, and the x-intercept of the tangent line x(n+1) is used as the new guess xn. Repeat as needed. xn will eventually converge to the root x.

newton_method_b.au3

Edited by clarinetmeister

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