This paper deals with the symmetric eigenvalue problem. An exact penalty function method is presented for solving the full eigenvalue and eigenvector problem. These algorithms amount to minimize convex functionals. Obviously, for dense problems, the symmetric QR method is superior to these algorithms. Therefore, these algorithms may be of particular assistence in the case of large sparse problems. By the way, a comparison with other methods (for example, the Lanczos method) is needed.
Reviewer: Liu Xinguo (Qingdao)