Least Squares Approximations, Gradient Flows and Double Bracket Equations

Dr. Tin-Yau Tam

Department of Mathematics
Auburn University

April 16, 1999

Abstract

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.