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#20835 / #1

Seit SoSe 2022

English

Numerical Linear Algebra

10

Liesen, Jörg

benotet

Mündliche Prüfung

Zugehörigkeit


Fakultät II

Institut für Mathematik

No information

Mathe

Kontakt


MA 3-3

Liesen, Jörg

liesen@math.tu-berlin.de

No information

PORD-Nr.ModultitelLPBenotungPrüfungsformPNr. (POS)Modulprüfung PORDModulprüfung PNr.
44132

Learning Outcomes

Students will be able to analyze and apply algorithms for solving numerical problems of linear algebra, in particular linear algebraic systems and eigenvalue problems.

Content

The course will cover the foundations of numerical linear algebra, including matrix decompsitions, perturbation theory and the basics of rounding error analysis. Several numerical methods for solving numerical problems of linear algebra will be discussed in detail. For linear algebraic systems the topics include direct and iterative methods, and structure-adapted solvers for special matrix classes. For eigenvalue problems the course will cover methods for full matrices (e.g., the QR algorithm) as well as for large and sparse matrices (e.g., the Lanczos and Arnoldi algorithms, and the Jacobi-Davidson method).

Module Components

Pflichtgruppe:

All Courses are mandatory.

Course NameTypeNumberCycleLanguageSWSVZ
Numerische Lineare Algebra/Numerical Linear Algebra (EN)VLWS/SSEnglish4
Numerische Lineare Algebra/Numerical Linear Algebra (EN)UEWS/SSEnglish2

Workload and Credit Points

Numerische Lineare Algebra/Numerical Linear Algebra (EN) (VL):

Workload descriptionMultiplierHoursTotal
180.0h(~6 LP)
Attendance15.04.0h60.0h
Pre/post processing15.08.0h120.0h

Numerische Lineare Algebra/Numerical Linear Algebra (EN) (UE):

Workload descriptionMultiplierHoursTotal
120.0h(~4 LP)
Attendance15.02.0h30.0h
Pre/post processing15.06.0h90.0h
The Workload of the module sums up to 300.0 Hours. Therefore the module contains 10 Credits.

Description of Teaching and Learning Methods

Lectures (4 hours per week) present the course material. They are accompanied by homework assignments and exercise sessions that discuss numerical examples and the solution of exercises.

Requirements for participation and examination

Desirable prerequisites for participation in the courses:

Desirable: Courses in Linear Algebra, Real Analysis, and Numerical Mathemtatics on the level of Lineare Algebra I+II, Analysis I+II, and Numerische Mathematik I at the TU Berlin.

Mandatory requirements for the module test application:

No information

Module completion

Grading

graded

Type of exam

Oral exam

Language

German/English

Duration/Extent

No information

Duration of the Module

The following number of semesters is estimated for taking and completing the module:
1 Semester.

This module may be commenced in the following semesters:
Winter- und Sommersemester.

Maximum Number of Participants

This module is not limited to a number of students.

Registration Procedures

Standard

Recommended reading, Lecture notes

Lecture notes

Availability:  unavailable

 

Electronical lecture notes

Availability:  unavailable

 

Literature

Recommended literature
G. H. Golub, C. F. Van Loan: Matrix Computations. Johns Hopkins University Press, 2013.
N. J. Higham: Accuracy and Stability of Numerical Algorithms. SIAM, 2002.
Y. Saad: Iterative Methods for Sparse Linear Systems. SIAM, 2003.
Y. Saad: Numerical Methods for Large Eigenvalue Problems. SIAM, 2012.
G. W. Stewart, J.-g. Sun: Matrix Perturbation Theory, Academic Press, 1990.
L. N. Trefethen, D. Bau III: Numerical Linear Algebra. SIAM, 1997.
J. W. Demmel: Applied Numerical Linear Algebra. SIAM, 1997.
R. A. Horn, C. J. Johnson: Matrix Analysis. Cambridge University Press, 2012.

Assigned Degree Programs


This module is used in the following Degree Programs (new System):

Studiengang / StuPOStuPOsVerwendungenErste VerwendungLetzte Verwendung
Scientific Computing (M. Sc.)11WiSe 2022/23WiSe 2022/23

Miscellaneous

No information