QR algorithms for non-symmetric eigenvalue problems
Special methods for symmetric eigenvalue problems (Jacobi-Iteration, Bisection, Divide & Conquer)
Computation of the singular value decomposition
QZ algorithms for generalized eigenvalue problems
Krylov subspace methods for large-scale eigenvalue problems
Jacobi-Davidson method for large-scale, generalized and polynomial eigenvalue problems
Preconditioned eigensolver
Methods for non-linear eigenvalue problems
Recommended literature
Börm, Mehl:Numerical Methods for Eigenvalue Problems, De Gruyter, 2012.
G. Golub, C. Van Loan:Matrix Computations, 3. Aufl., The John Hopkins University Press, 1996.
J. Demmel:Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997.
H.A. van der Vorst: Computational Methods for Large Eigenvalue Problems, S. 3-179 in P.G. Ciarlet, J.L. Lions (Hrsg.), Handbook of Numerical Analysis, Volume VIII, North-Holland (Elsevier), Amsterdam, 2002.
N. Trefethen, D. Bau, III.:Numerical Linear Algebra, SIAM, Philadelphia, 1997.
N. Trefethen, M. Embree:Spectra and Pseudospectra, Princeton Universty Press, 2005.