Georgia Institute of Technology College of Sciences

Inspired by the usefulness of difference of convex functions in some problems, e.g. sparse representations, we use such an idea of difference of convex functions to propose a method of finding an eigenfunction of a self-adjointoperator. In a matrix setting, this method always finds an eigenvector of a symmetric matrix corresponding to the smallest eigenvalue without solving Ax=b. In fact, such a matrix A is allowed to be singular, as well. We can apply the same setting to a generalized eigenvalue problem. We will discuss its convergence as well.