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

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.
• 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

Lectures + exercise sessions

Expected student activities

Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and programming assignments. Students also complete two substantial projects; the understanding of these projects will be verified during the exam.

Assessment methods

100% of the grade will be based on a written exam

Supervision

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

• Matrix computations / Golub
• Iterative methods for sparse linear systems / Saad
• Finite elements and fast iterative solvers / Elman

Notes/Handbook

Detailed lecture notes and slides will be provded on Moodle.

Moodle Link

• https://go.epfl.ch/MATH-453