Moses - Numerical Linear Algebra

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Module / Version:
#20835 / #1

Validity:
Seit SoSe 2022

Default display language:
English

Module title:
Numerical Linear Algebra

Credits:
10

Responsible person:
Liesen, Jörg

Grading:
benotet

Type of exam:
Mündliche Prüfung

Zugehörigkeit

Faculty:
Fakultät II

Institute:
Institut für Mathematik

Area of expertise:
No information

Prüfungsausschuss:
Mathe

Kontakt

Office:
MA 3-3

Contact person:
Liesen, Jörg

E-mail address:
liesen@math.tu-berlin.de

Website:
No information

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 Name	Type	Number	Cycle	Language	SWS	VZ
Numerische Lineare Algebra/Numerical Linear Algebra (EN)	VL		WiSe/SoSe	English	4
Numerische Lineare Algebra/Numerical Linear Algebra (EN)	UE		WiSe/SoSe	English	2

Workload and Credit Points

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

Workload description	Multiplier	Hours	Total
Attendance	15.0	4.0h	60.0h
Pre/post processing	15.0	8.0h	120.0h
			180.0h(~6 LP)

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

Workload description	Multiplier	Hours	Total
Attendance	15.0	2.0h	30.0h
Pre/post processing	15.0	6.0h	90.0h
			120.0h(~4 LP)

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:

This module has no requirements.

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 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

Semester:

Zeige auch ausgelaufene Studiengänge und StuPOs

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

Studiengang / StuPO	StuPOs	Verwendungen	Erste Verwendung	Letzte Verwendung
Mathematik (B. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Mathematik (M. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Scientific Computing (M. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Technomathematik (B. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Technomathematik (M. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Wirtschaftsmathematik (B. Sc.)	1	4	WiSe 2022/23	SoSe 2024
Wirtschaftsmathematik (M. Sc.)	1	4	WiSe 2022/23	SoSe 2024

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