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John-von-Neumann-Gastprofessur: Prof. Nick Trefethen Pfeil, Oxford University Pfeil

Von-Neumann Lecture Course: Approximation Theory and Approximation Practice

Prof. Trefethen

A course consisting of eight 90-minute weekly lectures beginning Monday 10 May 2010; 14:15–15:45, room MI 00.07.011.

This is a mathematics course for students and researchers interested in numerical computation. Familiarity with Matlab is essential. Some familiarity with approximation theory is desirable but not essential.

The course is built on an unusual book being completed by the lecturer with the title "Approximation Theory and Approximation Practice: A 21st-Century Treatment in the Form of 32 Executable Chebfun M-Files". It aims to teach both old and new ideas of univariate approximation of functions in a fresh and computational way, illustrating everything through the chebfun system (http://www.maths.ox.ac.uk/chebfun/). Both theorems and algorithms will be emphasized: for the former, always with reference to their originator whether in 1912 or 2004; for the latter, always in a hands-on and exploratory fashion.

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Topics to be treated include:

For Bachelor and Master students: The lecture has 3 ECTS. Successful attendance depends on the written solutions for the exercises given as homework assignements each week.

Solutions to Assignments

solns1.m solns1.pdf
solns2.m solns2.pdf
solns3.m solns3.pdf
solns4.m solns4.pdf
solns5.m solns5.pdf
solns6.m solns6.pdf
solns7.m solns7.pdf

Additional Reference

C. Runge, Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten Pfeil