On computing multi-dimensional generalized extreme and intermediate eigen subspaces

In this paper further analysis of the problem of deriving dynamical systems which converge to the minimum and maximum eigenpairs of a symmetric matrix simulaneously have been addressed. Systems that converge to intermediate subspaces are also developed. The derivation of these systems is based on optimizing constrained cost functions over high dimensional unit spheres. Thus necessary and sufficient conditions for optimality of smooth functions over spheres are first derived. In choosing certain cost function, the first order optimality conditions lead to solving a quadratic eigenvalue problem.