Numerical linear algebra

This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions and iterative methods, and eigenvalue computation will be introduced.

Numerical resolution of linear systems (problems, stability issues, and algorithmic complexity):

- matrix of elementary operations, LU factorization, and Choleski factorization

• Matrix standards, packaging
• Iterative methods: Jacobi, Gauss-Seidel
• Convergence analysis: spectral radius
• Overdetermined systems: least squares methods and applications.
• Singular value decomposition and applications.
• Calculation of eigenvalues. Location, link with the characteristic polynomial. Power and deflation methods.

HAX102X – Algebra I Linear Systems

HAX202X – Algebra II Vector Spaces and Linear Applications

HAX305X: Elementary Numerical Analysis

Recommended prerequisites: L1 math

Hourly volumes:

            CM: 15

            TD: 10.5

            TP: 15

            Land: