What Are the Rules for Diagonal Elements in LU Decomposition?

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Discussion Overview

The discussion revolves around the rules and conventions for diagonal elements in LU decomposition of matrices. Participants explore the requirements for the diagonal elements of the lower triangular matrix (L) and the upper triangular matrix (U), as well as the implications for different algorithms used in LU decomposition.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about whether the principal diagonal elements of L should be unity or if U should have unity diagonal elements.
  • Another participant references Wikipedia, noting that the factorization is unique if either L or U has diagonal elements of one.
  • A participant mentions that most algorithms they have encountered require L to have unity diagonal elements, but their specific problem necessitates U to have unity diagonal elements.
  • A participant shares a file for review, indicating a desire for feedback on their understanding or approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether L or U should have unity diagonal elements, and the discussion reflects multiple competing views on the matter.

Contextual Notes

The discussion highlights the lack of clarity regarding the requirements for diagonal elements in LU decomposition and the dependence on specific algorithms or applications.

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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