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
|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