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Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion
Author(s) -
Elsner Ludwig,
He Chunyang,
Mehrmann Volker
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.1680020207
Subject(s) - mathematics , norm (philosophy) , matrix norm , inverse , condition number , minification , dual norm , mathematical optimization , pure mathematics , eigenvalues and eigenvectors , normed vector space , law , physics , geometry , quantum mechanics , political science
We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.