Computing extreme subspaces using Mirsky theorem
Mohammed A. Hasan · 2009
Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.