A Geometrical Approach to Indefinite Least Squares Problems

Given Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and suffici...

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Detalles Bibliográficos
Autores principales:	Giribet, Juan Ignacio, Maestripieri, Alejandra Laura, Martínez Pería, Francisco Dardo
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2009
Materias:	Matemática Ciencias Exactas Least squares Oblique projections Selfadjoint operators Weighted generalized inverses
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/141580
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-141580
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Matemática Ciencias Exactas Least squares Oblique projections Selfadjoint operators Weighted generalized inverses
spellingShingle	Matemática Ciencias Exactas Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Giribet, Juan Ignacio Maestripieri, Alejandra Laura Martínez Pería, Francisco Dardo A Geometrical Approach to Indefinite Least Squares Problems
topic_facet	Matemática Ciencias Exactas Least squares Oblique projections Selfadjoint operators Weighted generalized inverses
description	Given Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and sufficient conditions for the existence of solutions of this abstract problem. Although the indefinite least squares problem has been thoroughly studied in finite dimensional spaces, the geometrical approach presented in this manuscript is quite different from the analytical techniques used before. As an application we provide some new sufficient conditions for the existence of solutions of an ℋ∞ estimation problem.
format	Articulo Articulo
author	Giribet, Juan Ignacio Maestripieri, Alejandra Laura Martínez Pería, Francisco Dardo
author_facet	Giribet, Juan Ignacio Maestripieri, Alejandra Laura Martínez Pería, Francisco Dardo
author_sort	Giribet, Juan Ignacio
title	A Geometrical Approach to Indefinite Least Squares Problems
title_short	A Geometrical Approach to Indefinite Least Squares Problems
title_full	A Geometrical Approach to Indefinite Least Squares Problems
title_fullStr	A Geometrical Approach to Indefinite Least Squares Problems
title_full_unstemmed	A Geometrical Approach to Indefinite Least Squares Problems
title_sort	geometrical approach to indefinite least squares problems
publishDate	2009
url	http://sedici.unlp.edu.ar/handle/10915/141580
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A Geometrical Approach to Indefinite Least Squares Problems

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