HI. First, thank you for your excellent tuturials. It has really made me understand how to invert a matrix. Just a query. Should X2 be 20.3962, as opposed from 19.6905? I've just been trying to work through your steps in excel. I get: (-96.208+(-1.56*1.085714))/-4.8 = 20.3962 Is the sign for -1.56 correct? If I use positive 1.56, I get your figure 19.6905. Or am I missing something here? I may be wrong, I have been before. :)
@uthmanzubairoluwatos You can look at playlists at the numericalmethodsguy channel for LU decomposition, or better yet go to the numericalmethods(.)eng(.)usf(.)edu site and click on videos. The list is given by topics.
When we use LU Decomposition to solve a system of equations, how do we guarantee its uniqueness? Will different LU Decompositions give different solutions to the same system of equations?
@sammyjny You can guarentee uniqueness by choosing 1 in the diagonal for all elements of L matrix. About the second question, the solutions for different LU decompositions is the same, provided the coefficient matrix is nonsingular.
@327372 Yes, if division by zero occurs while the coefficient matrix is nonsingular. If we change the rows for less round-off error or for avoiding division by zero, we follow the Gaussian Elimination with Partial Pivoting, and would get PA=LU, where P is called the perturbation matrix. Exchanging rows does not change the unknown vector.
that you a lot for making these videos...I forgot my book for a last overview before my exam. I went through examples online but they had the information scattered.
YOU ARE AWESOME...FROM UNIVERSITY OF GUELPH THANK YOU
AtlGBwoi 3 weeks ago
Thank you for your excellent introduction to LU decomposition. Very useful and easy to follow and understand! Greetings from Sweden!
fluffosoftisch 6 months ago
josh100ish 6 months ago
@josh100ish x2=(c2-a23*z3)/a22=(-96.208-(-1.56*1.085714))/(-4.8)=19.6905
numericalmethodsguy 6 months ago
@numericalmethodsguy
Ah, of course, double negatives...
Thanks for your quick reply. :)
josh100ish 6 months ago
Comment removed
josh100ish 6 months ago
how did he get the upper and lower matrix for the LU method because he did nt show how he get it here....................
uthmanzubairoluwatos 11 months ago
@uthmanzubairoluwatos You can look at playlists at the numericalmethodsguy channel for LU decomposition, or better yet go to the numericalmethods(.)eng(.)usf(.)edu site and click on videos. The list is given by topics.
numericalmethodsguy 11 months ago
thx alot Sir, this vedeo really helped me.
arjunvsthefirst 1 year ago
When we use LU Decomposition to solve a system of equations, how do we guarantee its uniqueness? Will different LU Decompositions give different solutions to the same system of equations?
sammyjny 1 year ago
@sammyjny You can guarentee uniqueness by choosing 1 in the diagonal for all elements of L matrix. About the second question, the solutions for different LU decompositions is the same, provided the coefficient matrix is nonsingular.
numericalmethodsguy 1 year ago
@numericalmethodsguy is partial pivoting necessary sometimes for LU factorization?
327372 8 months ago
@327372 Yes, if division by zero occurs while the coefficient matrix is nonsingular. If we change the rows for less round-off error or for avoiding division by zero, we follow the Gaussian Elimination with Partial Pivoting, and would get PA=LU, where P is called the perturbation matrix. Exchanging rows does not change the unknown vector.
numericalmethodsguy 8 months ago
that you a lot for making these videos...I forgot my book for a last overview before my exam. I went through examples online but they had the information scattered.
night03603 2 years ago
@night03603 You can look at playlists or go to the numericalmethods(.)eng(.)usf(.)edu site and click on videos. The list is given by topics.
numericalmethodsguy 1 year ago