ER02: Numerical Computing and Rigorous Numerical Computing (January 15-19, 2018)

Profs. Nick Trefethen and Warwick Tucker, 15-19 January 2018

This year, ENS-Lyon is hosting visiting professors who are leading experts in two aspects of numerical computing.
Nick Trefethen (University of Oxford) is a well-known numerical analyst and the inventor of Chebfun, a MATLAB-based tool that solves all kinds of problems of rootfinding, integration, and differential equations fast and typically to 15 digits of accuracy.
Warwick Tucker (Uppsala University) is a leader in the area of rigorous numerical computing, where instead of computing numbers with no guarantees, one applies interval analysis and other methods to obtain guaranteed results — and even to rigorously prove mathematical theorems with the aid of the computer.
In this week, using a mixture of lectures and hand-on computer laboratories, the two professors will showcase some of the highlights of these two sides of numerical computing.

Schedule for ER02

	8h15-10h	10h15-12h	14h15-16h	16h15-18h
Monday	Chebyshev (amphi B)	Chebyshev (lab rooms E001 and 125)	Validated numerics (amphi B)
Tuesday	Validated numerics (amphi B)	Validated numerics (amphi B)	Chebyshev (amphi B)	Chebyshev (lab rooms E001 and 125)
Wednesday	Chebyshev (amphi B)	Validated numerics (amphi B)	Validated numerics (amphi B)
Thursday	Validated numerics (amphi B)	Validated numerics (amphi B)
Friday	Chebyshev (lab rooms E001 and 125)	Chebyshev (amphi B)	Exam (amphi B)

For the part on Chebyshev:

• the text for this course is the first 6 chapters of the book Approximation Theory and Approximation Practice by Nick Trefethen, freely available at https://people.maths.ox.ac.uk/trefethen/ATAP;
• Lecture notes 1. Chebyshev points, interpolants, polynomials, and series
• Lecture notes 2. Analytic functions, Runge phenomenon, barycentric interpolation
• Lecture notes 3. Rootfinding, optimization, and quadrature
• Lecture notes 4. ODEs and Chebfun2
• software: Chebfun, a freely available package written in Matlab.

For the part on Validated Numerics:

• the text for this course is the book Validated Numerics: A Short Introduction to Rigorous Computations by Warwick Tucker,
  here is a shorter version;
• software: download and install Octave, scientific programming environment, whose syntax is largely compatible with Matlab, as well as the interval package and the symbolic package;
• computer lab no 1;
• automatic differentiation package for Octave;
• computer lab no 2