On Parlett's matrix norm inequality for the Cholesky decomposition
Alan S. Edelman, Walter F. Mascarenhas · Numerical Linear Algebra with Applications · 1995
Abstract We show that a certain matrix norm ratio studied by Parlett has a supermum that is O(\documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[\sqrt n \] $\end{document} ) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2‐norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.