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

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Recent Developments in Operator Theory and Its Applications

Part of the book series: Operator Theory Advances and Applications ((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.

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Author information

Authors and Affiliations

  1. Center for Control Engineering and Computation, Dept. of Electrical and Computer Engineering, University of California, Santa Barbara, CA, 93106, USA

    Ali H. Sayed

  2. Information Systems Laboratory, Dept. of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA

    Babak Hassibi

  3. Information Systems Laboratory, Dept. of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA

    Thomas Kailath

Authors
  1. Ali H. Sayed
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  2. Babak Hassibi
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  3. Thomas Kailath
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1NA, Canada

    P. Lancaster

  3. Department of Applied Mathematics and Institute of Industrial Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada

    P. N. Shivakumar

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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

  • eBook Packages: Springer Book Archive

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