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

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.