FSF3572 Approximation Theory 7.5 credits
This is a graduate course on numerical approximations of functions.
Information for research students about course offerings
The course will be given not 2018/19.
Content and learning outcomes
Course contents
The first part of the course mainly considers polynomial approximations and discusses issues related to convergence, accuracy, stability and complexity. The second part introduces various current topics in the field, such as wavelets, radial basis functions, sparse grid approximations and sparse L1 approximations.
Intended learning outcomes
After completing this graduate course the students will be able to understand and use basic methods and theory for numerical function approximation. In particular, the student should
- be able to use and analyze the basic methods for polynomial approximations (interpolation, least squares, piecewise approximations, Hermite interpolation)
- undestand and use the theory of convergence (Weierstrass) and best approximations for continuous functions as well as error estimates for smooth functions
- understand and use the theory of stability and conditioning for polynomial approximation methods, including its relation to interpolation points via Lebesgue constants
- understand and use the theory of orthogonal polynomials and Gauss quadrature methods
- have a good understanding of a couple of current topics in approximation theory, with a deeper knowledge of at least one of them.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics (including differential equations and numerical analysis).
Recommended prerequisites
Equipment
Literature
To be announced at least 4 weeks before course start at course home page.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- INL1 - Assignments, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework problems and a project.
Other requirements for final grade
Homework assignments and a final project should be completed to pass the course.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.