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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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