# Peter Arbenz: Catalogue data in Spring Semester 2015

Name | Prof. Peter Arbenz |

Address | Dep. Informatik ETH Zürich, CAB F 51.1 Universitätstrasse 6 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 74 32 |

arbenz@inf.ethz.ch | |

URL | http://www.inf.ethz.ch/personal/arbenz/ |

Department | Computer Science |

Relationship | Retired Adjunct Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

252-0504-00L | Numerical Methods for Solving Large Scale Eigenvalue Problems Does not take place this semester. | 4 credits | 3G | P. Arbenz | |

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 | ||||

252-5251-00L | Computational Science | 2 credits | 2S | P. Arbenz, T. Hoefler, P. Koumoutsakos | |

Abstract | Class participants study and make a 40 minute presentation (in English) on fundamental papers of Computational Science. A preliminary discussion of the talk (structure, content, methodology) with the responsible professor is required. The talk has to be given in a way that the other seminar participants can understand it and learn from it. Participation throughout the semester is mandatory. | ||||

Objective | Studying and presenting fundamental works of Computational Science. Learning how to make a scientific presentation. | ||||

Content | Class participants study and make a 40 minute presentation (in English) on fundamental papers of Computational Science. A preliminary discussion of the talk (structure, content, methodology) with the responsible professor is required. The talk has to be given in a way that the other seminar participants can understand it and learn from it. Participation throughout the semester is mandatory. | ||||

Lecture notes | none | ||||

Literature | Papers will be distributed in the first seminar in the first week of the semester | ||||

406-0663-AAL | Numerical Methods for CSEEnrolment only for MSc students who need this course as additional requirement. | 7 credits | 15R | P. Arbenz | |

Abstract | Introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. | ||||

Objective | * Knowledge of the fundamental algorithms in numerical mathematics * Knowledge of the essential terms in numerical mathematics and the techniques used for the analysis of numerical algorithms * Ability to choose the appropriate numerical method for concrete problems * Ability to interpret numerical results * Ability to implement numerical algorithms afficiently | ||||

Content | 1. Direct Methods for linear systems of equations 2. Interpolation 3. Iterative Methods for non-linear systems of equations 4. Krylov methods for linear systems of equations 5. Eigensolvers 6. Least Squares Techniques 7. Filtering Algorithms 8. Approximation of Functions 9. Numerical Quadrature 10. Clustering Techniques 11. Single Step Methods for ODEs 12. Stiff Integrators 13. Structure Preserving Integrators | ||||

Literature | W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006. M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002 C. Moler, Numerical computing with MATLAB, SIAM, 2004 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 | ||||

Prerequisites / Notice | A course covering the material is taught in German every autumn term (course unit 401-0663-00L). Exercises and examination are available in English. |