Solution of eigenvalue problems in Hilbert spaces by a gradient method

摘要

A gradient technique is developed for computing a class of nonisolated stationary points, called C-stationary points, for a real functional F defined on a Hilbert space.It is shown that the least-squares solutions of the operator equation Ax=b are C-stationary points for the functional (1/2)‖Ax−b‖2 when R(A) is closed and that certain eigenvectors of the general eigenproblem Ax=λBx are C-stationary points for the functional 1/2‖Ax−(/) Bx‖2. Numerical experiments are given to justify the results.