A Note on the Superoptimal Matrix Algebra Operators

Authors: Di Benedetto F.1; Serra Capizzano S.2

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 343-372(30)

Publisher: Taylor and Francis Ltd

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Abstract:

We study the superoptimal Frobenius operators in several matrix vector spaces and in particular in the circulant algebra, by emphasizing both the algebraic and geometric properties. More specifically we prove a series of "negative" results that explain why this approximation procedure is not competitive with the optimal Frobenius approximation, although it could be used for regularization purposes.

Keywords: Monotone homogeneous operators; Toeplitz matrices; Matrix vector spaces and matrix algebras; Preconditioning; Regularization

Document Type: Research article

Affiliations: 1: Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy 2: Dipartimento di Chimica, Fisica e Matematica, Via Valleggio 11, 22100 Como, Italy

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