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On Parlett's matrix norm inequality for the Cholesky decomposition
Author(s) -
Edelman Alan,
Mascarenhas Walter F.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020306
Subject(s) - cholesky decomposition , mathematics , matrix norm , norm (philosophy) , minimum degree algorithm , combinatorics , matrix (chemical analysis) , pure mathematics , algebra over a field , incomplete cholesky factorization , chemistry , physics , quantum mechanics , political science , law , eigenvalues and eigenvectors , chromatography
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.