Numerical Linear Algebra II (Eigenvalue Problems) WS 2013/14

Numerical Linear Algebra II (Eigenvalue Problems) WS2013/14

Lecture: Prof. Peter Benner Office Hours: on appointment
Tutoring: Heiko Weichelt Office Hours: on appointment

Schedule - Contents - Recommended literature - Handouts - Exercice sheets


Lecture: on Mondays, 3:00pm - 5:00pm     G02-210
on Tuesdays, 3:00pm - 5:00pm     G22A-105
Tutorial: on Wednesdays, 11:00am - 1:00pm     G05-211


  • 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.
  • G.W. Stewart: Matrix Algorithms
    • Volume I: Basic Decompositions
    • Volume II: Eigensystems
    SIAM, Philadelphia, 1998/2001.
  • Y. Saad: Numerical Methods for Large Eigenvalue Problems, Manchester University Press, 1992.
  • Z. Bau, J. Demmel, J. Dongarra, A. Ruhe, H.A. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia, 2000.


Exercise sheets

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