Numerical Linear Algebra
Instructor: Dr. Marin Sombra Gómez & Dr. Arturo VieiroCredits: 6 ECTS
Schedule: Wed 3pm-5pm / Fri 5pm-7pm
Semester: Fall
Course Outline:
- Standard Problems of Numerical Linear Algebra. General Techniques. Vector and Matrix Norms.
- Perturbation Theory. Gaussian Elimination.
- Error Analysis in Gaussian Elimination.
- Special Linear Systems.
- Linear Least Squares Problems. Normal Equations. QR Decomposition.
- Orthogonal Matrices. Householder Transformations. Givens rotations. Singular Value Decomposition.
- Principal Components Analysis.
- Google's PageRank algorithm.
- Algorithms for the Nonsymmetric Eigenproblem. Power Method.
- Canonical Forms. Computing Eigenvectors from the Schur Form. Inverse Iteration. Orthogonal Iteration.
- Iterative Methods for Linear Systems. Basic Iterative Methods. Jacobi's Method. Gauss Seidel Method. Successive Overrelaxation. Convergence of Jacobi's, Gauss-Seidel, and SOR(w) methods on the Model Problem. Detailed Convergence Criteria for Jacobi's, Gauss Seidel, and SOR(w) Methods.
- Algorithms for the Singular Value Decomposition. Tridiagonal and Bidiagonal Reduction. QR Iteration and Its Variations for the Bidiagonal SVD.