401-0663-00L  Numerical Methods for Computer Science

SemesterAutumn Semester 2022
LecturersR. Hiptmair
Periodicityyearly recurring course
Language of instructionEnglish


401-0663-00 VNumerical Methods for Computer Science
This course is designed in a flipped classroom format based on video tutorials and supplemented by a weekly question-and-answer session, for which attendance is highly recommended.
2 hrs
Thu10:15-12:00HG F 1 »
20.09.16:15-18:00HG F 1 »
27.09.16:15-18:00HG F 1 »
R. Hiptmair
401-0663-00 UNumerical Methods for Computer Science
Mon 10-12 or Mon 14-16 according to exercise group allocation.
2 hrs
Mon10:15-12:00CLA E 4 »
10:15-12:00LFW E 13 »
10:15-12:00ML H 41.1 »
10:15-12:00ML J 34.1 »
10:15-12:00ML J 34.3 »
14:15-16:00HG E 33.3 »
14:15-16:00LEE D 105 »
14:15-16:00LFW B 3 »
14:15-16:00LFW C 5 »
14:15-16:00ML F 40 »
R. Hiptmair
401-0663-00 PNumerical Methods for Computer Science
Self-study based on video tutorial and lecture notes.
2 hrs
04.11.14:15-16:00HG F 26.1 »
R. Hiptmair

Catalogue data

AbstractThe course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The course focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods in C++.
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
ContentFirst two weeks: A gentle introduction to C++

1. Computing with Matrices and Vectors
1.1 Fundamentals
1.2 Software and Libraries
1.4 Computational Effort
1.5 Machine Arithmetic and Consequences

2. Direct Methods for (Square) Linear Systems of Equations
2.1 Introduction: Linear Systems of Equations
2.3 Gaussian Elimination
2.6 Exploiting Structure when Solving Linear Systems
2.7 Sparse Linear Systems

3. Direct Methods for Linear Least Squares Problems
3.1 Least Squares Solution Concepts
3.2 Normal Equation Methods
3.3 Orthogonal Transformation Methods
3.3.1 Transformation Idea
3.3.2 Orthogonal/Unitary Matrices
3.3.3 QR-Decomposition
3.3.4 QR-Based Solver for Linear Least Squares Problems
3.4 Singular Value Decomposition

4. Filtering Algorithms
4.1 Filters and Convolutions
4.2 Discrete Fourier Transform (DFT)
4.3 Fast Fourier Transform (FFT)

5. Machine Learning of One-Dimensional Data
(Data Interpolation and Data Fitting in 1D)
5.1 Abstract Interpolation (AI)
5.2 Global Polynomial Interpolation

8. Iterative Methods for Non-Linear Systems of Equations
8.1 Introduction
8.2 Iterative Methods
8.3 Fixed-Point Iterations
8.4 Finding Zeros of Scalar Functions
8.5 Newton’s Method in Rn
8.6. Quasi-Newton Method
Lecture notesLecture materials (PDF documents and codes) will be made available to the participants through the course web page and online repositories. Access information will be communicated in the beginning of the course.
LiteratureU. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011.

A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000.

W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006.

W. Gander, M.J. Gander, and F. Kwok "Scientific Computing", Springer 2014.

M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002

P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002
Prerequisites / NoticeThe course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Familiarity with C++, object oriented and generic programming is an advantage. Participants of the course are expected to learn C++ by themselves, in case they do not know it already.
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Project Managementfostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
In examination block forBachelor's Degree Programme in Computational Science and Engineering 2016; Version 27.03.2018 (Examination Block G1)
Bachelor's Programme in Computational Science and Engineering 2012; Version 13.12.2016 (Examination Block G1)
ECTS credits7 credits
ExaminersR. Hiptmair
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 210 minutes
Additional information on mode of examinationMode of examination: written 180 minutes (leading to 210 minutes total exam time when adding the time reserved for reading the exam problems).

Computer based examination involving coding problems beside theoretical questions. Parts of the lecture documents and other materials will be made available on the computers during the examination.

An optional 30-minutes mid-term and an optional 30-minutes end-term exam will be held during the teaching period. The grades of these interim examinations will be taken into account through a BONUS of up to 30% for the final grade. The dates for the term exams will be communicated in the beginning of the course.
Written aidsNo aids admitted. Some documentations and documents will be made available on the exam computers.
Online examinationThe examination may take place on the computer.
Distance examinationIt is not possible to take a distance examination.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Main linkMoodle Page NumCS
Only public learning materials are listed.


401-0663-00 UNumerical Methods for Computer Science
Mon10:15-12:00CLA E 4 »
Mon10:15-12:00LFW E 13 »
Mon10:15-12:00ML J 34.1 »
Mon10:15-12:00ML H 41.1 »
Mon10:15-12:00ML J 34.3 »
Mon14:15-16:00ML F 40 »
Mon14:15-16:00HG E 33.3 »
Mon14:15-16:00LEE D 105 »
Mon14:15-16:00LFW B 3 »
Mon14:15-16:00LFW C 5 »


There are no additional restrictions for the registration.

Offered in

Computational Biology and Bioinformatics MasterTheoryWInformation
Computer Science BachelorBasic CoursesOInformation