13874 - Introduction to Numerical Linear Algebra Modulübersicht

Module Number: 13874
Module Title:Introduction to Numerical Linear Algebra
  Einführung in die Numerische Lineare Algebra
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr.-Ing. Oevermann, Michael
  • Prof. Dr. rer. nat. habil. Breuß, Michael
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Every summer semester
Credits: 6
Learning Outcome:After successful completion of the course the students know and understand classic and state of the art numerical methods and algorithms for solving linear systems of equations and to compute eigenvalues and eigenvectors. Through programming exercises they have acquired the practical skills to implement and validate numerical methods for scientific computing applications. The students have learned to use the programming language Python and common Python libraries/toolboxes (Numpy, Scipy) for an efficient and performant    implementation methods used in scientific computing.

Contents:The module focuses on methods and algorithms suitable for solving linear sets of equations as they typically arise in many applications such as solving/discretzising partial differential equations in engineering sciences or machine learning algorithms. In particular we will cover:
  • Classic iterative methods for solving linear systems of equations (Jacobi, Gauß-Seidel, SOR)
  • Projection type methods for solving linear systems of equations (CG, GMRES)
  • Direct methods for sparse linear systems of equations
  • Jacobi eigenvalue algorithm, power iteration, QR iteration
Additionally, we will address practical issues of solving large sparse systems of linear equations such as storage schemes and parallelisation strategies.



Recommended Prerequisites:Basic knowledge of mathematics as conveyed by mathematical courses in computer science or engineering from the first three to four semesters, e.g.:
  • Module 11101 Lineare Algebra und analytische Geometrie I, and  
  • Module 11103 Analysis I
or
  • Module 11112 Mathematik IT-1 (Diskrete Mathematik)
  • Module 11113 Mathematik IT-2 (Lineare Algebra)
  • Module 11213 Mathematik IT-3 (Analysis)
or
  • Module Höhere Mathematik - T1
  • Module 11108 Höhere Mathematik - T2
  • Module 11206 Höhere Mathematik - T3
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 2 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 120 Hours
Teaching Materials and Literature:
  • G. H. Golub, C. F. van Loan: Matrix Computations
  • L. N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM
  • Y. Saad: Iterative Methods for Sparse Linear Systems
  • T. A. Davis: Direct Methods for Sparse Linear Systems
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of exercises in the course
Final module examination:
  • Oral exam, 30 min. OR
  • Written exam, 90 min.
In the first lecture it will be announced, if the examination will be offered in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2019
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Master (research-oriented) / Künstliche Intelligenz Technologie / PO 2022
  • Master (research-oriented) / Physics / PO 2021
Remarks:
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Numerics“
  • Study programme Informatik B.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“
  • Study programme Informatik M.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“
  • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex  „Advanded Methods“
  • Study programme  Künstliche Intelligenz Technologie M.Sc.: Compulsory elective module in complex „Software-basierte Systeme“
  • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
Module Components:
  • Lecture: Introduction to Numerical Linear Algebra
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
Phase-out Module: Follow-up Module since: 17.11.2022