401-3650-72L Rational Approximation and Interpolation
| Semester | Autumn Semester 2022 |
| Lecturers | R. Hiptmair |
| Periodicity | non-recurring course |
| Course | Does not take place this semester. |
| Language of instruction | English |
| Abstract | The seminar covers theory and algorithms for rational interpolation based on classical and modern literature. The various topics have to be presented by groups of students. | ||||||||||||||||||||||||
| Objective | Participants of the seminar should acquire familiarity with the theoretical properties of approximation by means of rational functions as well as knowledge about algorithms used for computing approximating or interpolating rational functions. | ||||||||||||||||||||||||
| Content | The simplest and most widely used function system for approximation in computational mathematics are polynomials. They are ideally suited for smooth (analytic) functions. However, in many application we encounter functions with kinks and other kinds of singularities. In this case approximation by rational functions, that is, quotients of polynomials, may be vastly superior. This is why rational approximation and interpolation is receiving increased attention for the construction of surrogate models in model order reduction. This seminar will study a number of research papers dealing with both theoretical and algorithmic aspects of rational approximation and interpolation. | ||||||||||||||||||||||||
| Literature | Will be announced in due course | ||||||||||||||||||||||||
| Prerequisites / Notice | Good skills in analysis are required as well as basic familiarity with numerical methods for interpolation and approximation with polynomials. Preparatory meeting: Mon, Sep 19, 2022, 18:00 on ZOOM, Meeting ID: 698 4220 0325, Password: RAP HS22 Every presentation has to be done jointly by a group of 2-3 students with presenters selected at random. Every participant will have to present on 2-3 occasions. See https://people.math.ethz.ch/~hiptmair/Seminars/RAP_22/SeminarRAP_HS22.pdf for more information. | ||||||||||||||||||||||||
Competencies |
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