Numerical Analysis, Root-Finding, and Mathematics lessons. Code for the channel is hosted on GitHub (github.com/osveliz/numerical-veliz). You can leave a topic request in the video comments or preferably in the GitHub forum. Support the channel by becoming a GitHub Sponsor (github.com/sponsors/osveliz).
This is a concern for Newton's Method (and others) as well. The paper doesn't address it but a common technique is to shift the x value by some tiny random complex number.
I am trying to solve a problem where optimum ( minimum) of the function is required a= a(d) P = P(a,d) In the solution we are assuming some value of d . Value of 'a' is obtained. Since a ,d are known, P can be calculated and hence the function.
This is such a wonderful video and I love your presentation! I especially love the fractal part. I think my only criticism is that you sometimes mumble words too quickly (e.g. you occasionally say "pomial" when you say "polynomial") and I had to rewind a few times to catch what you were saying. But ignoring that, your video is really good and I could follow along without getting lost.
thank you for this nice video It's nice to see these and try implementing them afterwards actually I think it is one of the best way to learn a new language, making something useful in it I will try to implement it in Mojo
Finally. It was worth the wait. Finally we have a video explaining Jenkins-Traub in the best way possible! And this is the first time I actually see the fractal from the method... ever!
A nice idea for a new video that would connect well to this one: Explain the ITP method, which has recently been adapted in many root solving libraries. Instead of making Newton's method secure, it is making bisection fast (without losing the worst-case behaviour). Also interesting is Chandrupatla's method, which has an inbuilt way to decide when to bisect and when to use quadratic inverse interpolation.
@5:00 the reality is that none of them discovered differential calculus. The person who discovered it was Madhava from India in 1300. It's well know that intelectual property was subtracted from Kerala and these dudes managed to understand it 200 or 300 years later. All credits go to India.
I would really like to see a proof of why Horner scheme gives the quotient. I understand why it gives the remainder of division, but it giving the quotient looks like magic. I saw some proofs by solving equations for polynomial coefficients, but I wonder if there's a quick and simple argument, at least for low degrees like 2 and 3.
I want to a video of how regula falsi is mathematically same like regula falsi can be converted to secant method so they are mathematically same you why we call a secant method a contribution how these two are different
Can't believe how few views this has for just have fantastic it is, needed to find a simple and fast method for computing minima today, and this video explained exactly what was needed in a mere few minutes. Otherwise it would have taken much longer for me to be sure of what I was doing, thank you so much!
The method is not well known which leads to not being used much. Seems like every numerical methods textbook covers fixed point iteration, but then stops there without going over Wegstein or Steffensen.
You elucidate the method effortlessly in such simple words. This channel is pretty helpful in helping me, a beginner easily grasp the steps of these methods, found it jus now.
Oscar, I wish your videos were more popular. We give millions of views to other RU-vidrs that deal with content that is as captivating as useless. On the other hand, you deal with actual problems that can be encountered in school or at work. You provide simple and effective explanations, resources, and code. This is a very pragmatic and scientist oriented approach. No fricking fireworks and smoke, and this penalizes you. I hope that real life rewards you as you deserve. Keep up the good work!!
one of the best iteration theorem is banach's fixed point theorem which is great for all the continued fraction and continued root because they all satisfy the conditions for the theorem
