# Thread: Numerical Analysis problem

1. ## Numerical Analysis problem

Let $PAQ = LR$ be the triangular descomposition with Pivot's search strategy in the remaining matrix $A\in\mathbb R^{n\times n}$. Prove that for $A^{ - 1} = (a_{ij}^{*})$,

$
\big|a_{ij}^{*}\big|\le n\cdot2^{2n - 4}\max\Bigg\{\frac1{|r_{11}|},\ldots,\frac1{|r_{nn }|}\Bigg\}.
$