The first method you described is called the Steepest Descent (not the Gradient Descent). Gradient Descent is the simplest one, the Steepest Descent is an improvment on the Gradient Descent, exactly as you described.
What I don't understand is: why use an iterative process if we know that there's exactly one minimum, just set the gradient to 0 and solve the resulting system of equations, no?
those methods are used when you have let say 10^6+ equations (for example in Finite Element Method). With those method you solve in much faster then by setting all derivatives equal to 0. Even it seems there you need all steps to get to minimum its not true, usually you are close enought even in those humangus number of equations to minimum that you are already satisfied with answer that you dont need rest of 95% of missing gradients, and thats why those methods are so powerfull,.
I made the video for a class. I guess I didn't expect it to get so many views and comments especially for people to keep watching it after some years. But if theres alot of interest I can make another video. Do you have any suggestions for topics?
It’s okay... It’s too slow at the beginning and too fast at the end. And why would you start with gradient descent? I would think that most people studying cg are already miles beyond gradient descent, have seen Newton’s method and now study Newton-like methods.
You don't use your mathematics for resolve all the problema. If you have problems with more than 3 variables, not is possible look the solution if not used the abstract mathematics. A mutli dimensional problems i.e. chemical problems (pressure, tempeture, flux, composition and rate) only is visualized with math, not with graph. Used you mathematics and numbers
![[CFD] Conjugate Gradient for CFD (Part 1): Background and Steepest Descent](http://i.ytimg.com/vi/jXShvxPcRl4/mqdefault.jpg)
![[CFD] Conjugate Gradient for CFD (Part 1): Background and Steepest Descent](/img/tr.png)
Here is 2021, your class is still great for now. ❤️
You are a life saver! I have an assignment that's related to this method and I understood it pretty well! THANK YOU!
Thank you for making this video!! It's really helpful with my studies :)
good video, but you used the Laplace operator instead of the nabla operator for the gradient.
The first method you described is called the Steepest Descent (not the Gradient Descent). Gradient Descent is the simplest one, the Steepest Descent is an improvment on the Gradient Descent, exactly as you described.
Very very clear and helpful， thank you very much
Good video, clear explanation.
Good job, Priya, elegant explanation!
Another interesting topic is Newton-CG and what to do if the Hessian is indefinite.
Excellent stuff. Really helped
Please note that x* is the minimizer and the minimum.
Great video!
great video. Thanks!!
thank you very much
What is a TOD?
how is the value of alpha1 updated..
What I don't understand is: why use an iterative process if we know that there's exactly one minimum, just set the gradient to 0 and solve the resulting system of equations, no?
those methods are used when you have let say 10^6+ equations (for example in Finite Element Method). With those method you solve in much faster then by setting all derivatives equal to 0. Even it seems there you need all steps to get to minimum its not true, usually you are close enought even in those humangus number of equations to minimum that you are already satisfied with answer that you dont need rest of 95% of missing gradients, and thats why those methods are so powerfull,.
@@mrlolkar6229 Yeah, I kinda figured it out now.
Many thanks!
gold
is alpha_k a matrix or scalar quantity?
scalar... i just didn't flatten my residual (which was a matrix in my case)
lack of detailed explanation and hard to understand
low volume
Sorry! Something was missing in my last comment. Please note that x* is the minimizer and NOT the minimum.
+Aboubekeur Hamdi-Cherif yeap same notice
hmm, that means x1 = x0 + x*
right?
🍵
Please can you share the code
I dont understand how you updated alpha1.
alpha1 is calculated in 7:42, in this case d1= -grad(f) = b-A*x
wow interesting how she made one technical video and stopped. Motivation was lost I guess?
Have you not seen Bear and Simba dumbass?
@@nickp7526 I said technical video my dear chap.
@@AdityaPrasad007 Think he was joking bruh
@@ethandickson9490 really? I'm pretty bad at sarcasm... @Nick was it a joke?
I made the video for a class. I guess I didn't expect it to get so many views and comments especially for people to keep watching it after some years. But if theres alot of interest I can make another video. Do you have any suggestions for topics?
It’s okay... It’s too slow at the beginning and too fast at the end. And why would you start with gradient descent? I would think that most people studying cg are already miles beyond gradient descent, have seen Newton’s method and now study Newton-like methods.
cute lecture :P
I like fud
You don't use your mathematics for resolve all the problema. If you have problems with more than 3 variables, not is possible look the solution if not used the abstract mathematics. A mutli dimensional problems i.e. chemical problems (pressure, tempeture, flux, composition and rate) only is visualized with math, not with graph. Used you mathematics and numbers
Great video!