Awesome video! Thank you! Great work as usual. Highly appreciate this. Very interesting ❤️
@David-cx3fc
2 жыл бұрын
Wow, thanks for the great video! You explained that so well and made it easy to understand
@Icenri
Жыл бұрын
Thanks!
@jacknguyen5220
2 жыл бұрын
Multivariate bisection is no doubt quite an oof. Not something I'd want to implement myself tbh. In contrast, I've found that interval analysis is a godsend which surpasses bracketing methods, generalizes easily to multidimensional problems, can perform optimization, and even works on a globalized scale opposed to a localized one (e.g. finding ALL roots of a polynomial). Although it comes with extra computational cost, it's insanely easy to implement usually, if you're willing to forego the need to re-implement everything by using round-up and round-down variants for truly guaranteed bounds. I've also been planning on writing a paper based on the idea but without using interval analysis (directly). Although it lacks the same guarantees as stuff like here, it has probabilistic guaranteed convergence, performs well in even say 1000 dimensions, and is very easy to implement and understand.
@fish830911
2 жыл бұрын
May I ask what is the interval analysis?
@jacknguyen5220
2 жыл бұрын
@@fish830911 The basic idea is that you can write functions to accept multiple inputs (like x from 2 to 3, denoted x = [2, 3]) at the same time and get a range of possible outputs (like x^2 from 4 to 9, denoted [2, 3]^2 = [4, 9]) at the same time. This way it should be obvious that root-finding boils down to checking if 0 is in the range of possible outputs, and the multi-dimensional case is just checking along each dimension.
@sexynoobda449
2 жыл бұрын
Can you make a video on the graphs of different rate of convergences like sublinear, linear, etc. and how they are dependent upon the number of iterations. You can also discuss about the convexity or concavity of the convergence graphs because even though it is a very fundamental thing but I am quite sure that many people don't know about convergence and their study and not much is readily available on the internet itself.
@OscarVeliz
2 жыл бұрын
I have a video discussing rate of convergence, although not related to convexity/concavity. If you like to check it out kzitem.info/news/bejne/q4qf1JmmfaBil34 and give me some feedback, I would greatly appreciate it. I also made another video that touches on sublinear convergence kzitem.info/news/bejne/04V41WWskJ-jhII in the context of a series.
@sifatahmed1413
Ай бұрын
How will we know the root we are looking for in the Triangle?
@OscarVeliz
Ай бұрын
The triangle test only tells you if [0,0] is inside, it doesn't tell you which input value leads to that result.
@救命-t6g
7 ай бұрын
there are too-scarce sources discussing error terms and error analaysis mid-terms and finals ever propose these forgettable error problems
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