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...
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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678019_v111_n1_p65_Giribet http://hdl.handle.net/20.500.12110/paper_01678019_v111_n1_p65_Giribet |
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paper:paper_01678019_v111_n1_p65_Giribet2023-06-08T15:16:56Z A geometrical approach to indefinite least squares problems 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678019_v111_n1_p65_Giribet 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 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. |
| 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 |
2010 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678019_v111_n1_p65_Giribet http://hdl.handle.net/20.500.12110/paper_01678019_v111_n1_p65_Giribet |
| _version_ |
1768542882876096512 |