As you all know, I like the Newton-Raphson method. And so, explaining it covers quite a few articles on this website. Still, there is more we can do to explain this method. There is always more. To do that, I once again enlisted my academic colleague ChatGPT, and...
Solving Equations
The Newton-Raphson method, narrated in the style of a Film Noir Voiceover
You may have seen my post on the Newton-Raphson method in the style of the King-James version of the Bible. Since that turned out very well, I asked ChatGPT to explain the method again to me, but this time in the style of a Film Noir Voiceover. Here is the result....
The Newton-Raphson method according to the King-James version of the Bible
I've been experimenting with ChatGPT quite a bit lately (let's be honest, who hasn't). And at some point, I had the idea to ask ChatGPT to explain the Newton-Raphson method to me. But, as you have seen here on ComputingSkillset.com, I have quite some experience using...
How to Find the Initial Guess in Newton’s Method
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 Explained: Details, Pictures, Python Code
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...
11 Highly Instructive Examples for the Newton Raphson Method
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...
Newton Fractals Explained: Examples and Python Code
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...