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The Kähler Structure of the Total Least Squares Problem, Brockett’s Steepest Descent Equations, and Constrained Flows

  • Anthony M. Bloch
Part of the Progress in Systems and Control Theory book series (PSCT, volume 3)

Abstract

In this paper we show how the Total Least Squares identification problem may be viewed as a steepest descent problem on a Kähler manifold. The Kähler structure gives a method of explicitly deriving the steepest descent equations from a corresponding Hamiltonian flow associated with the problem. In the line-fitting case the steepest descent flow itself is shown also to be equivalent to the flow of a constrained Hamiltonian system — the Toda system.

Keywords

Steep Descent Symplectic Form Gradient Flow Toda Lattice Grassmann Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Anthony M. Bloch

There are no affiliations available

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