# 252-0504-00L Numerical Methods for Solving Large Scale Eigenvalue Problems

Semester | Spring Semester 2015 |

Lecturers | P. Arbenz |

Periodicity | two-yearly recurring course |

Course | Does not take place this semester. |

Language of instruction | English |

Abstract | In this lecture algorithms are investigated for solving eigenvalue problems with large sparse matrices. Some of these eigensolvers have been developed only in the last few years. They will be analyzed in theory and practice (by means of MATLAB exercises). |

Objective | Knowing the modern algorithms for solving large scale eigenvalue problems, their numerical behavior, their strengths and weaknesses. |

Content | The lecture starts with providing examples for applications in which eigenvalue problems play an important role. After an introduction into the linear algebra of eigenvalue problems, an overview of methods (such as the classical QR algorithm) for solving small to medium-sized eigenvalue problems is given. Afterwards, the most important algorithms for solving large scale, typically sparse matrix eigenvalue problems are introduced and analyzed. The lecture will cover a choice of the following topics: * vector and subspace iteration * trace minimization algorithm * Arnoldi and Lanczos algorithms (including restarting variants) * Davidson and Jacobi-Davidson Algorithm * preconditioned inverse iteration and LOBPCG * methods for nonlinear eigenvalue problems In the exercises, these algorithm will be implemented (in simplified forms) and analysed in MATLAB. |

Lecture notes | Lecture notes, Copies of slides |

Literature | Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000. Y. Saad: Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester, 1994. G. H. Golub and Ch. van Loan: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore 1996. |

Prerequisites / Notice | Prerequisite: linear agebra |