Course Description
1. Matrix factorizations.
2. Perturbation and error analysis.
3. Operation cost and convergence rate.
4. Direct Methods for linear systems.
5. LU and Cholesky factorizations.
6. Perturbation and error analysis.
7. Vector and matrix norms.
8. Perturbation analysis for linear systems.
9. Error analysis.
10. Classical iterative methods.
11. Jacobi and Gauss-Seidel method.
12. Convergence analysis.
13. SOR method.
14. Krylov subspace methods.
15. Steepest descent method.
16. Conjugate gradient method.
17. Practical CG method and convergence analysis.
18. Preconditioning.
19. GMRES method.
Intended Learning Outcomes
CILO-1: Apply the basic concepts of numerical linear algebra, particularly in the area of matrix factorizations.
CILO-2: Interpret the definition of generalized inverses, devise appropriate strategies to solve linear systems with multiple solutions.
CILO-3: Analyse the perturbation errors for linear systems and least squares problems.
CILO-4: Apply iterative methods for solving linear systems.