UAH > Math > Colloquia > 4/16/1999
A general setting of least squares approximations with orbital constraints is formulated. A unified extension of the gradient flows and the double bracket equations of Chu-Driessel and Brockett is obtained. In particular, Chu-Driessel's differential equation associated with singular value decomposition is viewed as a double bracket equation. Extrema of the optimization problems are given. Some results can be extended to Eaton Triple which is evolved from probability inequalities and optimization.