Large-scale complex eigenvalue problems (Q1262079)

The author gives a review about methods for solving eigenvalue problems. At first some results of linear algebra, necessary for solving linear systems of equations and eigenvalue problems, are presented. General methods (QR-, QZ-algorithm) for solving eigenvalue problems are briefly discussed, whereas methods suitable for large-scale problems by preserving the sparseness of the matrices are detailedly described (vector iteration, inverse vector iteration, Lanczos algorithm, Rayleigh quotient iteration, initial-value formulation). Some considerations concerning software and hardware are presented. At last applications in quantum mechanics, hydrodynamics and plasma physics are discussed.