Computational linear algebra
Summary
This course provides an overview of advanced techniques for solving large-scale linear algebra problems, as they typically arise in applications. A central goal of this course is to give the ability to choose a suitable solver for a given application.
Content
Introduction
Sources of large-scale linear algebra problems. Recap of required linear algebra concepts.
Eigenvalue problems
Krylov subspace methods. Singular value problems. Preconditioned iterative methods.
Linear systems
Direct sparse factorizations. Krylov subspace methods and preconditioners.
Matrix functions
Theory and algorithms.
Keywords
linear systems, eigenvalue problems, matrix functions
Learning Prerequisites
Required courses
Linear Algebra, Numerical Analysis
Learning Outcomes
By the end of the course, the student must be able to:
- Choose method for solving a specific problem.
- Prove the convergence of iterative methods.
- Interpret the results of a computation in the light of theory.
- Implement numerical algorithms.
- Describe methods for solving linear algebra problems.
- State theoretical properties of numerical algorithms.
Teaching methods
Ex cathedra lecture, exercises in the classroom and with computer
Expected student activities
Attendance of lectures.
Completing exercises.
Completing a miniproject.
Solving problems on the computer.
Assessment methods
Miniproject and oral examination.
Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.
Resources
Bibliography
Lecture notes will be provided by the instructor. Complimentary reading:
H. Elman, D. J. Silvester, and A. J. Wathen. Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Oxford University Press, 2005.
G. H. Golub and C. Van Loan. Matrix computations. Johns Hopkins University Press, 1996.
Y. Saad. Iterative methods for sparse linear systems. Second edition. SIAM, 2003.
Ressources en bibliothèque
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Computational linear algebra
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines