General information 
Course unit name: Numerical Linear Algebra
Course unit code: 572661
Academic year: 20192020
Coordinator: Arturo Vieiro Yanes
Department: Faculty of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture with practical component 
30 

 ITbased class 
30 
Supervised project 
40 
Independent learning 
50 
Teaching blocks 
1. Basic definitions
1.1. Vectors and matrices. Rank and nullspace. Norms.
1.2. Eigenvalues and eigenvectors.
1.3. Linear systems.
1.4. Stability. Condition number. Complexity of an algorithm.
1.5. Structured matrices. Blocking algorithms.
2. Linear systems
2.1. Gaussian methods, LU, Cholesky.
2.2. Orthogonalization methods: QR factorization (GramSchmidt, Householder). Application to the least squares problem (LSP).
2.3. Iterative methods: Jacobi, GaussSeidel, successive overrelaxation method (SOR).
2.4. Introduction to Krylov methods (Lanczos, Arnoldi, GMRES,...)
3. Eigenvalues and eigenvectors
3.1. Power method
3.2. LR and QR iteration
4. Singular value decomposition (SVD).
4.1. Singular values and vectors.
4.2. Applications to LSP and graphic compression.
4.3. Principal component analysis (PCA).
Teaching methods and general organization 
The teaching methodology consists of:
During the lectures, the lecturer will explain the definitions and main results of the syllabus, which will be illustrated with examples. Several practical situations, exercises and implementation tricks will be discussed. During the semester some short projects will be stated. The students should work around each project and implement the codes needed to solve the proposed exercises. A short summary of the methods used and the results obtained will be required for grading, as well as the codes implemented. 
Official assessment of learning outcomes 
To succeed in the assessment of the subject, students must show a good understanding of the foundations of the algorithms presented in the lectures, including coding details of the algorithms, and a good ability to solve concrete problems.
Examinationbased assessment Students who wish to opt for a single assessment must inform the Secretary by the date set in the Faculty calendar.

Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Saad, I. Iterative methods for sparse linear systems. Philadelphia : SIAM, 2003.