Using the Method Example 1 (derivative of the function is known): By repeating this process (perform iterations) better and better approximations of the value for x are obtained. If you start with a known derivative and function value you can calculate a new prediction. The method is depicted in the figure below: Fig 1) Depiction of Newton-Raphson MethodĮquation 2 pretty much sums up the method. Which we can rearrange to get the “Newton-Raphson Formula”: This point gives an improved estimation of the root. The basics of the method come from the fact that the first derivative is equivalent to the slope and therefore if you know it, you can calculate the tangent intersection: If you have an initial guess at some point,, the tangent can be extended to some point that crosses 0 at an easily calculable point. AKA you want to find the roots of the equation. The Newton-Raphson method is used when you have some function f(x) and you want to find the value of the dependent variable (x) when the function equals zero. You probably don’t need to know all of them (just pick a few that work for you!) Typically I stick to the Newton-Raphson method and the bisection method and I rarely have problems. What is the Newton-Raphson method? Basically it is an iterative approach for solving the roots of functions. Introduction to the Newton-Raphson Method ![]()
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