LU decomposition of matrix

[Muthuraj R]

Actually I am new to this topic.
I read few tutorials about LU decomposition of matrix in the net.
A = LU ; A - actual matrix, L - Lower triangular matrix, U - Upper triangular matrix.Few people say that, principal diagonal elements of L should be unity.
Some others say that, principal diagonal elements of U should be unity.
Pls clarify.
or else suggest me some suitable method for LU decomposition of a matrix.
Thanks.

 

[chiro]

Hey Muthuraj B and welcome to the forums.

Have you looked at Wikipedia?

http://en.wikipedia.org/wiki/LU_decomposition

 

[Muthuraj R]

Thanks, chiro.
Wikipedia says,
"The factorization is unique if we require that the diagonal of L (or U) consist of ones."
Fine. Either 'L' or 'U' has to have unity diagonal elements.
Algorithms for LU decomposition that I can see in the net follows 'L' to have unity diagonal elements. But my problem requires 'U' to have unity diagonal elements.
Could pls suggest such algorithm.

 

[Muthuraj R]

Ya. Got it.
Attached that file.
Pls check and correct me if anything is wrong.
Thanks all.

 

[blue_raver22]

Hi there, don't worry if you are new to this topic, it can be complex and confusing at first. LU decomposition is a method used to factorize a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). This can be useful in solving systems of linear equations and in other mathematical operations. The principal diagonal elements of L and U do not necessarily have to be unity, but it is common to choose them to be unity for simplicity and convenience. The important thing is that the product of L and U should equal the original matrix A.

As for a suitable method for LU decomposition, there are a few options such as Gaussian elimination, Crout's method, and Doolittle's method. It is best to choose a method that suits your specific problem and data. I suggest you continue to study and practice with different methods to gain a better understanding of LU decomposition. Good luck!