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Inertia conditions for the minimization of quadratic forms in indefinite metric spaces. (English) Zbl 0863.93091

Gohberg, I. (ed.) et al., Recent developments in operator theory and its applications. Proceedings of the international conference, Winnipeg, Canada, October 2-6, 1994. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 87, 309-347 (1996).
Using results on indefinite metric space theory, two minimization problems are considered. Under a fundamental set of inertia conditions, a complete link between both solutions can be established. A very nice translation of prediction and filtering notions in the language of indefinite metric notions can be found. Applications to \(H^\infty\) filtering and approximate total least squares methods are presented.
For the entire collection see [Zbl 0840.00035].

MSC:

93E24 Least squares and related methods for stochastic control systems
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.)

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