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 necess...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Giribet, J.I., Maestripieri, A., Martínez Pería, F.
Formato:	JOUR
Materias:	Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Analytical techniques Estimation problem Existence of Solutions Finite dimensional space Indefinite least squares Least Square Self adjoint operator Sufficient conditions Weighted generalized inverse Hilbert spaces Vector spaces
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01678019_v111_n1_p65_Giribet
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01678019_v111_n1_p65_Giribet
record_format	dspace
spelling	todo:paper_01678019_v111_n1_p65_Giribet2023-10-03T15:05:21Z A geometrical approach to indefinite least squares problems Giribet, J.I. Maestripieri, A. Martínez Pería, F. Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Analytical techniques Estimation problem Existence of Solutions Finite dimensional space Indefinite least squares Least Square Oblique projections Self adjoint operator Sufficient conditions Weighted generalized inverse Hilbert spaces Vector spaces 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. © 2009 Springer Science+Business Media B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01678019_v111_n1_p65_Giribet
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Analytical techniques Estimation problem Existence of Solutions Finite dimensional space Indefinite least squares Least Square Oblique projections Self adjoint operator Sufficient conditions Weighted generalized inverse Hilbert spaces Vector spaces
spellingShingle	Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Analytical techniques Estimation problem Existence of Solutions Finite dimensional space Indefinite least squares Least Square Oblique projections Self adjoint operator Sufficient conditions Weighted generalized inverse Hilbert spaces Vector spaces Giribet, J.I. Maestripieri, A. Martínez Pería, F. A geometrical approach to indefinite least squares problems
topic_facet	Least squares Oblique projections Selfadjoint operators Weighted generalized inverses Analytical techniques Estimation problem Existence of Solutions Finite dimensional space Indefinite least squares Least Square Oblique projections Self adjoint operator Sufficient conditions Weighted generalized inverse Hilbert spaces Vector spaces
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. © 2009 Springer Science+Business Media B.V.
format	JOUR
author	Giribet, J.I. Maestripieri, A. Martínez Pería, F.
author_facet	Giribet, J.I. Maestripieri, A. Martínez Pería, F.
author_sort	Giribet, J.I.
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
url	http://hdl.handle.net/20.500.12110/paper_01678019_v111_n1_p65_Giribet
work_keys_str_mv	AT giribetji ageometricalapproachtoindefiniteleastsquaresproblems AT maestripieria ageometricalapproachtoindefiniteleastsquaresproblems AT martinezperiaf ageometricalapproachtoindefiniteleastsquaresproblems AT giribetji geometricalapproachtoindefiniteleastsquaresproblems AT maestripieria geometricalapproachtoindefiniteleastsquaresproblems AT martinezperiaf geometricalapproachtoindefiniteleastsquaresproblems
_version_	1807322583231627264

A geometrical approach to indefinite least squares problems

Ejemplares similares