Numerical algorithms [ LINMA2710 ]
5.0 crédits ECTS
30.0 h + 22.5 h
2q
| Teacher(s) |
Van Dooren Paul ;
|
| Language |
English
|
Place
of the course |
Louvain-la-Neuve
|
| Main themes |
- Quantitative study of floating point rounding errors
- Specification of the notions of "numerical stability" and "conditioning"
- Development of iterative methods and convergence criteria that are computer-independent
- Examples of complexity analysis of algorithms
- Development of high performance parallel algorithms
|
| Aims |
To strengthen the know-how in "scientific computing'' via a critical analysis of algorithms and via the development of state-of-the-art algorithms in numerical analysis, that have a good performance on modern computing platforms.
|
| Content |
- Qualitative analysis of rounding errors
- Definition of numerical stability and conditioning
- Convergence of iterative algorithms
- Critical analysis of classical algorithms illustrating basic concepts
- LU factorization of matrices
- Iterative refinement
- Bloc methods and parallel algorithms
- Algorithms for polynomials
- Fast matrix multiplication
- Fast Fourier Transform
|
| Other information |
Prerequisites:
Basic knowledge (1st cycle) in numerical analysis and programming (MATLAB)
Evaluation:
Theoretical exercises and MATLAB exercises count together for 15% of the final score. The written exam amounts for 85% of the final score.
Supporting material:
Typeset course notes complemented by the book: Nick Higham, "Accuracy and Stability of Numerical Algorithms", SIAM Publications, Philadelphia, 1995
|
Cycle et année
d'étude |
> Master [120] in Mathematical Engineering
> Master [120] in Computer Science
> Master [120] in Computer Science and Engineering
|
Faculty or entity
in charge |
> MAP
|
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