Artículos de revistas
A geometrical approach to indefinite least squares problems
Fecha
2010-06Registro en:
Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo; A geometrical approach to indefinite least squares problems; Springer; Acta Applicandae Mathematicae; 111; 1; 6-2010; 65-81
0167-8019
CONICET Digital
CONICET
Autor
Giribet, Juan Ignacio
Maestripieri, Alejandra Laura
Martinez Peria, Francisco Dardo
Resumen
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 h B(Cu − y), Cu − y i = minx∈H h B(Cx − y), Cx − y i, 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 sufficient conditions for the existence of solutions of some H∞ estimation problems.