Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue problems, describes some techniques for solving them, and addresses the diiculties and challenges which ar...

The computation of a few eigenvalues and the corresponding eigenvectors of large complex non hermitian matrices arises in many applications in science and engineering such as magnetohydrodynamic or electromagnetism [6], where the eigenvalues of interest often belong to some region of the complex plane. If the size of the matrices is relatively small, then the problem can be solved by the standa...

We discuss several techniques for nding leading eigenvalues and eigenvectors for large sparse matrices. The techniques are demonstrated on a scalar Helmholtz equation derived from a model semiconductor rib waveguide problem. We compare the simple inverse iteration approach with more sophisticated methods, including minimum degree reordering, Arnoldi and Lanczos methods. We then propose a new Ar...