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Inertia Conditions for the Minimization of Quadratic Forms in Indefinite Metric Spaces

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Part of the Operator Theory Advances and Applications book series (OT,volume 87)

Abstract

We study the relation between the solutions of two minimization problems with indefinite quadratic forms. We show that a complete link between both solutions can be established by invoking a fundamental set of inertia conditions. While these inertia conditions are automatically satisfied in a standard Hilbert space setting, which is the case of classical least-squares problems in both the deterministic and stochastic frameworks, they nevertheless turn out to mark the differences between the two optimization problems in indefinite metric spaces. Applications to H-filtering, robust adaptive filtering, and approximate total-least-squares methods are included.

Keywords

  • Quadratic Form
  • Block Diagonal Matrix
  • Quadratic Cost Function
  • Inertia Condition
  • Gramian Matrix

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Sayed, A.H., Hassibi, B., Kailath, T. (1996). Inertia Conditions for the Minimization of Quadratic Forms in Indefinite Metric Spaces. In: Gohberg, I., Lancaster, P., Shivakumar, P.N. (eds) Recent Developments in Operator Theory and Its Applications. Operator Theory Advances and Applications, vol 87. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9035-9_15

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  • DOI: https://doi.org/10.1007/978-3-0348-9035-9_15

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9878-2

  • Online ISBN: 978-3-0348-9035-9

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