Numerical Linear Algebra for engineers

Information

Teacher coordinator	Benoît Gaüzère
Teacher(s)	Gilles Gasso, Benoît Gaüzère
Language	French
Credits	4.5
Teaching	Lectures : 21h Exercises : 42h
Web site	https://moodle.insa-rouen.fr/course/view.php?id=159

Aim and objective

This course is designed to acquaint students in engineering with the fundamental theory of matrix calculus and associated basic numerical algorithms.

Outcome learning

INSA reference data :
- Maîtriser les outils mathématiques de base [3P]
- Maîtriser un langage de haut niveau [3P]
CNISF reference data :
- J10C [2I]
- J10G [2I]

1 - Notion, 2 - Concept, 3 - Application, I - fully, P - incomplete

Course description

This first part of the course is devoted to the solution of systems of linear equations, covering the following topics: classical matrix factorizations including LU, Cholesky, QR factorizations and their application to linear system solving and least squares problems. The second part of the course covers iterative methods, condition and stability, error analysis of linear systems solution. Finally eigenvalue problems, singular value decomposition and related computation algorithms are introduced.

Prerequisites

Notions of matrix and vector space

Bibliography

Numerical Recipies in C and the Art of Scientific Computing, 1992, Cambridge University Press
P. LASCAUX & R. THEODOR : Analyse numérique matricielle appliquée à l'art de l'ingénieur, Tomes 1 et 2, Masson.
Burden & Faires, Numerical Analysis, Brooks and Cole, 1997
Golub, G. H., & Van Loan, C. F. (2012). Matrix computations (Vol. 3). JHU Press.

Assessment

Mid term exam: 40 %
Final exam: 60%