UCL - Numerical algorithms

[INMA2710]

[30h + 22.5h] 5 credits

This course is taught in the 1st semester.

Teacher(s): Paul Van Dooren

Language: French

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

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.

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

Content and teaching methods

- 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 (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

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