Thank you very much... But I have one question. If I use algorithm, which is in video at 42:21 , algorithm works perfect for squared matrix A. If I used matrix A as A = [1 2 3; 4 5 6] (which is rectangular matrix, with less rows than columns) than algorithm crush. If I use traditional Matlab function [Q, R] = qr(A) , it gives correct solution. Please can you somebody explain why, or make a correction of algorithm ? Thank you
the problem is you don't have R[i:, i] to work with anymore after the mth column, therefore, to make householder work, I think you can just skip the columns after the mth
If I have to write the code for QR decomposition I really will not want to multiply by H matrices This explanation is insufficient for programmers who write the codes for numerical linear algebra
@@hugginb5929 but if you are capable to write your own pseudo code you dont need to watch this video There is no need for multiplication by H matrix For matrices of sizes l x m and m x n standard multiplication takes O(l*m*n) and O(m x n) extra space but multiplication by H matrices can be done cheaper for both time and space complexity He didn't show effective way to multiply by H matrices so this video is useless and waste of time so anyone who want to code QR will waste 46 min of his life if he watch this video
@UCNbJkcasubFH_C4cZLDCSlQ In book written in my native language reduction to Hessenberg form by Gaussian elimination is well described and i had no problems to write code for it I multiplied matrix by some rotation matrices from both left and right and also i was able to write code for QR using rotations While calculation approximated value of eigenvalues i met following problems 1. How to choose shift well 2. Slow convergence for repeated roots 3. How to use deflation 4. Stop crititerion other than maximum number of iterations
Gotta admit im impressed with the content this university puts out. Phenomenal this is free.
This comment is to appreciate and encourage you to continue making videos like this.
For me; this is the most elegant explanation of QR & Householder
agree. watched several videos on this, first one that clicked
What an amazing teacher! Thank you for putting these videos online.
From Belgium here, very good explanation! Keep it up
great video. very clear explanation with great examples. spent a lot of time lost before i found this
This was very very helpful! Thank you, Prof Kutz
OMG! what an amazing video. Your explanation for this concept is top-notch
Very dynamic and practical teaching :)
Thanks Prof Kutz!
very clear teachings, thx for professor
This is very helpful. Thank you, Prof Kutz
also love that he is wearing a coat!!!
Thanks for the explanation.
Do you show me how to find the documents about topic of this video? I thanks a lot and this is a great video.
Thank you very much... But I have one question. If I use algorithm, which is in video at 42:21 , algorithm works perfect for squared matrix A.
If I used matrix A as A = [1 2 3; 4 5 6] (which is rectangular matrix, with less rows than columns) than algorithm crush. If I use traditional Matlab function [Q, R] = qr(A) , it gives correct solution. Please can you somebody explain why, or make a correction of algorithm ? Thank you
the problem is you don't have R[i:, i] to work with anymore after the mth column, therefore, to make householder work, I think you can just skip the columns after the mth
Like a true mentat, he drinks coffee while lecturing.
thanks you alot :)
thank you !
Here is a list of the whole series of videos on Applied Linear Algebra: ua-cam.com/play/PLFB8R5rtkrDrcuIyA1vKAr9F1s-aETOJ3.html&si=dXl6UYEGpti-l1CE
If I have to write the code for QR decomposition I really will not want to multiply by H matrices
This explanation is insufficient for programmers who write the codes for numerical linear algebra
Can you please give me link of any such video? Thanks
@@hugginb5929 but if you are capable to write your own pseudo code you dont need to watch this video
There is no need for multiplication by H matrix
For matrices of sizes l x m and m x n
standard multiplication takes O(l*m*n) and
O(m x n) extra space
but multiplication by H matrices can be done cheaper
for both time and space complexity
He didn't show effective way to multiply
by H matrices so this video is useless and waste of time
so anyone who want to code QR will waste 46 min of his life if he watch this video
@UCNbJkcasubFH_C4cZLDCSlQ In book written in my native language reduction to Hessenberg form by Gaussian elimination is well described and
i had no problems to write code for it
I multiplied matrix by some rotation matrices from both left and right and also
i was able to write code for QR using rotations
While calculation approximated value of eigenvalues i met following problems
1. How to choose shift well
2. Slow convergence for repeated roots
3. How to use deflation
4. Stop crititerion other than maximum number of iterations