Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/16396
Title: Improving approximate inverses based on Frobenius norm minimization
Authors: González, Luis 
Suárez Sarmiento, Antonio F. 
UNESCO Clasification: 120111 Teoría de matrices
120610 Matrices
12 Matemáticas
Keywords: Approximate inverses
Frobenius norm minimization
Trace
Spectrum
Singular values
Normal equations
Issue Date: 2013
Journal: Applied Mathematics and Computation 
Abstract: Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R n×n , among all matrices belonging to certain subspaces of R n×n , are obtained. Particularly, a natural generalization of the classical normal equations of the system Ax = b is given, when searching for approximate inverses N 6= AT such that AN is symmetric and kAN − IkF < AAT − I F …
URI: http://hdl.handle.net/10553/16396
ISSN: 0096-3003
DOI: 10.1016/j.amc.2013.03.057
Source: Applied Mathematics and Computation[ISSN 0096-3003],v. 219, p. 9363-9371
Rights: by-nc-nd
Appears in Collections:Artículos
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