LU Decomposition Method: Finding Inverse of a Matrix: Example

[Jcx4ds]

Thanks! You will save my test. ^^

[Ec0topia]

THANKS!!!! BIG TIME!!! :-D!!!

[hesdjjim]

Thanks so much! This is in my textbook, but the textbook skips steps! :(

[ProxySpam]

Can you help me? I try to figure out Thomas algorithm for tri-diagonal matrix. It sais 1. decomposition 2. forward substitution and 3. back substitution.

They give no examples but I find good similarities with what you did in this video. Some insights? Ty!

[numericalmethodsguy]

@ProxySpam It is very similar, but one has to take advantage of the sparseness (zero entries) of the matrix. For example, in the 1st step of FE, you only need to make A(2,1) to be zero, others are already zero. This is again true for 2nd step of FE where only A(3,2) needs to be made zero. Hence L will only have the non-zeros only in diagonal and lower subdiagonal. For U, there will be nonzeros only diagonal and upper subdiagonal elements.

[ProxySpam]

@numericalmethodsguy Sounds pretty much the same to me. So if in the exam they ask to use thomas method and I use the method above will I lose points? lol

[numericalmethodsguy]

@ProxySpam It is the same from an exam point to find the inverse. But if you are finding the solution of a set of equations, the following algorithm is used - see Wikipedia and search for Tridiagonal matrix algorithm. A matlab program is written there.

[327372]

@numericalmethodsguy the LU method to find matrix inverse takes more time than using cofactor expansion. why do we need to learn this method? decomposing [A] into [L] and [U] is time consuming. I am sure there are less time consuming methods to find inverse

[numericalmethodsguy]

@327372 Time taken by cofactor may seem small for small nxn matrix when done by hand. But from a computational time perspective - for large n, the time taken by cofactor method is huge as compared to LU. The time for LU decomposition method may be 32/3*T*n^3 (T=clock cycle) for large n, and for cofactor method may be T*n*n! for large n. See what happens for n=50, 500, 5000.

[carnatic1987]

this was really useful and i understood math for a change!!!thanks a lot!!!

[Varegous]

Why didn't my school hire you?!?!

Alot more helpful than my teachers! Thank you so much for making these videos!!

[tabadam87]

Have exam tomorrow from it. Hope it will help me :) THX @numericalmethodsguy !

[zildjian]

Thanks, this'll help me a lot :D Greetings from Spain!