# RootFinding Demo

Posted by **Will Campbell**,

Teja is making a comeback after his 2011 Sudoku Pick of the Week. This time, he has created a wonderful little Newton-Raphson app. For anyone who's taken a numerical methods class, you are probably familiar with this technique for finding a value for

*x*that satisfies equation

*f(x) = 0*. But if you're new to the concept, Wikipedia has a great article on the subject.

In essence, this algorithm starts with an initial guess for the value of

*x*. If

*f(x)*equals zero, then lucky you, you're done. If not, you calculate the derivative of the function and use that to aim yourself towards a better guess for the value of

*x*. You repeat this process with your new value of

*x*, and after a few iterations, you hopefully converge on

*f(x) = 0*. In the image below, you see how we approach the zero-crossing of the blue line (our

*f(x)*) with several Newton-Raphson iterations (the red lines).

It turns out that this is a screenshot from Teja's root finding app. The user interface enables you to symbolically express your equation. You specify your initial guess and number of iterations; the app will then present you the solution. What's really fun about this is that you can click on the figure and instantaneously get results for a new initial guess. This interaction is quite instructive in the effectiveness yet limitations of this root finding method. I enjoyed experimenting with functions that weren't continuously differentiable. Oftentimes, my results would be unstable, but every once in a while, I could still achieve convergence.

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