Peter Arbenz: Catalogue data in Spring Semester 2018

Name Prof. em. Peter Arbenz
E-mailarbenz@inf.ethz.ch
URLhttp://www.inf.ethz.ch/personal/arbenz/
DepartmentComputer Science
RelationshipRetired Adjunct Professor

NumberTitleECTSHoursLecturers
252-0504-00LNumerical Methods for Solving Large Scale Eigenvalue Problems Information
The course will be offered for the last time.
4 credits3GP. Arbenz
AbstractIn 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).
ObjectiveKnowing the modern algorithms for solving large scale eigenvalue problems, their numerical behavior, their strengths and weaknesses.
ContentThe 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 notesLecture notes,
Copies of slides
LiteratureZ. 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 / NoticePrerequisite: linear agebra
252-5251-00LComputational Science
Takes place for the last time.
2 credits2SP. Arbenz, P. Chatzidoukas
AbstractClass 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.
ObjectiveStudying and presenting fundamental works of Computational Science. Learning how to make a scientific presentation.
ContentClass 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 notesnone
LiteraturePapers will be distributed in the first seminar in the first week of the semester