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, iterative methods, and eigenvalue calculation will be introduced.

Numerical Solution of Linear Systems (Problems, Stability Issues, and Algorithmic Complexity):

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

• Matrix standards, packaging
• Iterative Methods: Jacobi, Gauss-Seidel
• Convergence Analysis: Spectral Radius
• Overdetermined Systems: Least-Squares Methods and Applications.
• Singular Value Decomposition and Its Applications.
• Calculation of eigenvalues. Location, relationship to the characteristic polynomial. Power and deflation methods.

HAX102X – Algebra I: Linear Systems

HAX202X – Algebra II: Vector Spaces and Linear Mappings

HAX305X: Elementary Numerical Analysis

Recommended prerequisites: First-year math

Hourly volumes:

            CM: 15

            TD: 10.5

            TP: 15

            Lot: