Course Syllabus for

Numerical Approximation
Numerisk approximation

NUMN19F, 7.5 credits

Valid from: Spring 2021
Decided by: Professor Thomas Johansson
Date of establishment: 2020-09-24

General Information

Division: Numerical Analysis
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: NUMN19
Teaching language: English


The overall goal of the course is to provide an introduction to classical results and numerical algorithms within approximation theory and prepare the participants for further studies in mathematics and computationally oriented subjects. The purpose is further to develop the participants' ability to solve problems, communicate mathematical reasoning, assess mathematical algorithms and translate them into effective code.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must be able to argue for the importance of approximation theory as a tool in mathematics,computational technology and related subjects.

Course Contents

The course treats: • The approximation problem: Norms, approximation spaces, the Weierstrass theorem. • Theory of best approximation in Euclidean spaces: Existence, uniqueness, characterisation theorems, duals. • Construction of best approximations: Orthogonality, Chebyshev polynomials, Haar spaces, the exchange algorithm.

Course Literature

Iske, A.: Approximation Theory and Algorithms for Data Analysis. Springer, 2019. ISBN 9783030052270.

Instruction Details

Types of instruction: Lectures, miscellaneous. Theoretical and practical assignments.

Examination Details

Examination formats: Oral exam, written assignments
Grading scale: Failed, pass

Admission Details

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

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