Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion | Zendy

Elsner Ludwig | Zendy; He Chunyang | Zendy; Mehrmann Volker | Zendy

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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.

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