Let $A$ be symmetric positive definite matrix, and LU decompose it. Then we get $A = LL^T$.
The growth factor of matrix A is as follows
$$ \rho \equiv \frac{\max _{i, j}\left|u_{i j}\right|}{\max _{i, j}\left|a_{i j}\right|} $$
A textbook said that $\rho = 1$, but I don't know how to prove it.
Would anybody elaborate this?
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alryosha
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Probably, $\rho \leq 1$ – uranix Jul 15 '20 at 16:55