Newton Raphson Method Review

is so small (e.g., 0.00001) that you’ve reached your desired level of precision. Why Use It? (The Pros)

The magic of the method lies in calculus. It assumes that if you zoom in close enough to a curve, it looks like a straight line. By using the at a specific point, we can follow that line down to the x-axis to find a "better" guess for the root. The Formula Starting with an initial guess , the next approximation is calculated as: newton raphson method

xn+1=xn−f(xn)f′(xn)x sub n plus 1 end-sub equals x sub n minus the fraction with numerator f of open paren x sub n close paren and denominator f prime of open paren x sub n close paren end-fraction : Your current guess. : The value of the function at that guess. : The derivative (slope) of the function at that guess. How the Algorithm Works (Step-by-Step) Choose an initial value that you think is close to the root. is so small (e

Use the formula to see where the tangent line hits the x-axis. This is your new guess ( Repeat: Plug back into the formula to get Stop: Keep going until the difference between xn+1x sub n plus 1 end-sub It assumes that if you zoom in close

Imagine you want to find the square root of 10. This is equivalent to solving Guess: Let’s start at Iteration 1: Iteration 2:

The Newton-Raphson method is an iterative technique used to find the (or zeros) of a function . A root is simply the value of