On the evaluation of selected eigenpairs of large matrices based on function optimization algorithms

Large scale matrix diagonalization is reviewed and analysed in the context of normal function optimization techniques. The problem of obtaining high roots is discussed at length. The rational function optimization procedure and Taylor techniques are presented. It is demonstrated that these algorithms make it possible to obtain any desired eigenpair in an efficient way. Finally, the possibility of using a fixed subspace dimension during the diagonalization iterative process is discussed. To this end a short review is presented of the use of update Hessian matrices to diagonalize large matrices.