401-3650-72L  Rational Approximation and Interpolation

SemesterAutumn Semester 2022
LecturersR. Hiptmair
Periodicitynon-recurring course
CourseDoes not take place this semester.
Language of instructionEnglish

AbstractThe 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.
ObjectiveParticipants 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.
ContentThe 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.
LiteratureWill be announced in due course
Prerequisites / NoticeGood 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.
Subject-specific CompetenciesConcepts and Theoriesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Media and Digital Technologiesassessed
Social CompetenciesCommunicationassessed
Cooperation and Teamworkassessed
Personal CompetenciesCritical Thinkingassessed
Self-awareness and Self-reflection assessed