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

Chapter

## 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
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## Copyright information

© Birkhäuser Boston 1990