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Numerical analysis [ LINMA1170 ]

5.0 crédits ECTS 30.0 h + 22.5 h 1q

Teacher(s)	Van Dooren Paul (coordinator) ; Absil Pierre-Antoine ;
Language	French
Place of the course	Louvain-la-Neuve
Main themes	Numerical solution on non-linear equations: location of real and complex zeros of a polynomial, iterative methods and convergence theorems. Numerical solution of linear systems : iterative methods (conjugate gradients, Jacobi, Gauss-Seidel, Krylov methods), preconditioning. Numerical solution of ordinary differential equations : multistep methods, stability analysis, stiff differential equations.
Aims	To better understand numerical methods for solving equations and to analyze their numerical properties such as convergence and stability. Equations solvers include finding zeros, solving systems of equations and solving ordinary differential equations.
Content	1. Location of the roots of a polynomial 2. Approximation via fixed point iteration 3. Bernoulli method and the QD algorithm 4. Iterative methods for large scale systems 5. Ordinary differential equations
Other information	Prerequisites: First cycle level in numerical calculus and programming. Support: many references are used and mentioned during the course.
Cycle et année d'étude	> Master [120] in Mathematics > Master [60] in Mathematics > Master [120] in Statistics: General > Bachelor in Engineering > Bachelor in Computer Science > Bachelor in Mathematics > Master [120] in Mechanical Engineering > Master [120] in Electro-mechanical Engineering > Master [120] in Physical Engineering > Master [120] in Computer Science and Engineering > Master [120] in Computer Science
Faculty or entity in charge	> MAP

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