What Are the Rules for Diagonal Elements in LU Decomposition?

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SUMMARY

The discussion centers on the rules for diagonal elements in LU decomposition, specifically whether the principal diagonal elements of the lower triangular matrix (L) or the upper triangular matrix (U) should be unity. Consensus indicates that while many algorithms standardize L to have unity diagonal elements, there are scenarios where U can also be required to have unity diagonal elements. The unique factorization condition for LU decomposition allows for either matrix to have unity diagonals, depending on the algorithm used.

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  • Understanding of matrix factorization concepts
  • Familiarity with LU decomposition terminology
  • Basic knowledge of triangular matrices
  • Experience with numerical algorithms for matrix operations
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  • Research algorithms that allow U to have unity diagonal elements in LU decomposition
  • Explore numerical stability considerations in LU decomposition
  • Learn about the implications of choosing L or U for unity diagonal elements
  • Study the implementation of LU decomposition in numerical libraries like NumPy or MATLAB
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Mathematicians, computer scientists, and engineers involved in numerical analysis, particularly those working with matrix computations and algorithms for LU decomposition.

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

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