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401-0663-00L 7 Credits BSC , MSC D-BSSE , D-INFK
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Numerical Methods for Computer Science

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
VVZ CR 2.66

Last Updated: 2026-02-05 15:48:24

Abstract

The 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

Content

* Computing with Matrices and Vectors 2.1 Fundamentals 2.2 Software and Libraries 2.4 Computational Effort 2.5 Machine Arithmetic and Consequences * Direct Methods for (Square) Linear Systems of Equations 3.1 Introduction: Linear Systems of Equations (LSE) 3.2 Theory: Linear Systems of Equations (LSE) 3.5 Survey: Elimination Solvers for Linear Systems of Equations 3.7 Sparse Linear Systems * Direct Methods for Linear Least Squares Problems 4.1 Least Squares Solution Concepts 4.2 Normal Equation Methods 4.3 Orthogonal Transformation Methods 4.3.1 Transformation Idea 4.3.2 Orthogonal/Unitary Matrices 4.3.3 QR-Decomposition 4.3.4 QR-Based Solver for Linear Least Squares Problems 4.4 Singular Value Decomposition (SVD) 4.5 SVD-Based Optimization and Approximation * Filtering Algorithms 5.1 Filters and Convolutions 5.2 Discrete Fourier Transform (DFT) 5.3 Fast Fourier Transform (FFT) * Machine Learning of One-Dimensional Data (Data Interpolation and Data Fitting in 1D) 6.1 Abstract Interpolation (AI) 6.2 Global Polynomial Interpolation 6.4 Splines 6.7 Least Squares Data Fitting * Iterative Methods for Non-Linear Systems of Equations 9.2 Iterative Methods 9.4 Finding Zeros of Scalar Functions 9.5 Newton's Method in Rn 9.7 Non-linear Least Squares

Resources

Lecture Notes

Lecture 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.

Literature

U. 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

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 225 minutes
Aids
No aids admitted.
Digital
The exam takes place on devices provided by ETH Zurich.
Mode of examination: written 180 minutes (leading to 225 minutes total exam time when adding the time reserved for reading the exam problems).Computer based examination involving coding problems beside theoretical questions. Partsof the lecture documents and other materials will be made available online during theexamination.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.

Course Components

Type Title Time & Place Hours
lecture Numerical 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.
  • Thu 10:15-12:00 (HG F 1)
2 h weekly
exercise Numerical Methods for Computer Science
Groups are selected in myStudies. Mon 10-12 or Mon 14-16 according to exercise group allocation.
  • Mon 10:15-12:00 (CLA E 4)
  • Mon 10:15-12:00 (LFW E 13)
  • Mon 10:15-12:00 (ML H 41.1)
  • Mon 10:15-12:00 (ML J 34.1)
  • Mon 10:15-12:00 (ML J 34.3)
  • Mon 14:15-16:00 (HG E 33.3)
  • Mon 14:15-16:00 (LEE D 105)
  • Mon 14:15-16:00 (LFW B 3)
  • Mon 14:15-16:00 (LFW C 5)
  • Mon 14:15-16:00 (ML F 40)
2 h weekly
practical/laboratory course Numerical Methods for Computer Science
Self-study based on video tutorial and lecture notes.
No time listed 2 h weekly

Offered In