Why people make and use LDU factorization?
I think LU factorization and PA = LU are enough to solve equation.
Anyone know why?
Why we use LDU factorization rather than LU factorization?
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linear-algebra
lu-decomposition
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0Have you looked at the $LDL^T$ factorization? See also https://en.wikipedia.org/wiki/Cholesky_decomposition. – 2017-01-03
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0@J W very good, thanks – 2017-02-06
1 Answers
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Expanding on what J W linked, let the matrix be positive definite be such that it can be represented as a Cholesky decomposition, $A = LL^{-1}$, we can determine that $L_{11} = \sqrt{A_{11}}$
If we instead let $A = LDL^{-1}$, we can instead set the diagonal of $L$ to unity and let $D_{11} = A_{11}$
This produces the same result but allows us to avoid having to compute $\sqrt{A_{11}}$