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You understand how the Newton-Raphson method works, but don't know which \(x_0\) to use? I know exactly what you mean. So how do you find the best initial guess for Newton's method? There is no general answer that fits all concrete cases or problems. As a...

Newton's method for numerically finding roots of an equation is also known as the Newton-Raphson method. Recently, I asked myself how to best explain this interesting numerical algorithm. Here I have collected a couple of illustrated steps that clearly show how...

Newton's method for numerically finding roots of an equation is most easily understood by example. At least, I learn more easily from examples. So, perhaps you do, too. In this article I've collected a couple of highly instructive examples for the Newton-Raphson...

We've seen fractals as (mostly) beautiful pictures showing bizarre structures in different colors. Some of them are generated by a mathematical algorithm called the Newton-Raphson method. But what are Newton fractals? Newton fractals are fractals created in the plane...