Unit NUMERICAL APPROXIMATION AND APPLICATIONS
- Course
- Mathematics
- Study-unit Code
- 55A00049
- Curriculum
- Matematica per l'economia e la finanza
- Teacher
- Bruno Iannazzo
- Teachers
-
- Bruno Iannazzo
- Bruno Iannazzo
- Hours
- 12 ore - Bruno Iannazzo
- 35 ore - Bruno Iannazzo
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2020/21
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/08
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian or English (if all students agree).
- Contents
- Selected topics in Numerical Analysis related to approximation, linear algebra and non-linear optimization and their applications.
- Reference texts
- For the numerical analysis topics:
J. Stoer, R. Bulirsch. Introduction to numerical analysis. Springer. 2013;
material provided by the teacher.
For the optional topics, we will use a specific reference, that will be communicated during the lectures. - Educational objectives
- Get into mathematical aspects related to some important applications. Getting in touch with all mathematical modeling aspects: abstraction, modelisting interpretation, computer simulation.
- Teaching methods
- Face-to-face lectures and laboratory sessions.
- Learning verification modality
- Oral exam and seminar. The oral exam can be substituted by a project or a seminar, upon availability.
- Extended program
- Spline interpolation. B-splines. Trigonometric interpolation. Fast Fourier Transform. Least square approximation and singular value decomposition. Matrices with positivity structure, eigenvalue computation, matrix functions and matrix means. Non-linear and manifold optimization.
During the course , some applications will be taken into account: centrality in complex networks, search engines, Markov chains ans queueing models, data fitting, digital filtering, curves and surfaces in computer graphics; quantum information theory.