Unit NUMERICAL APPROXIMATION AND APPLICATIONS

Course
Mathematics
Study-unit Code
55A00087
Curriculum
Didattico-generale
Teacher
Bruno Iannazzo
Teachers
  • Bruno Iannazzo
Hours
  • 47 ore - Bruno Iannazzo
CFU
6
Course Regulation
Coorte 2021
Offered
2022/23
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
English (or Italian if all students require it).
Contents
Selected topics in Numerical Analysis related to approximation, linear algebra and non-linear optimization and their applications to data science and information technologies.
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 data science and information technologies applications. Getting in touch with all mathematical modeling aspects: abstraction, modelisting interpretation, computer simulation (using the software Matlab or Octave).
Prerequisites
Numerical analysis (e.g. LU factorization, interpolation theory). Linear algebra, calculus with several real variables. Elementary computer science. The optional part may have different prerequisites (e.g. differential geometry).
Teaching methods
Face-to-face lectures and laboratory sessions, using Matlab/Octave.
Learning verification modality
The exams consists in a detailed discussion of some topics of the course. In the evaluation, the comprehension will be priviledged with respect to the memorization. The exam's duration is about one hour.

For students attending the course, the exams will have two terms:
- mid-term, where the student will give a seminar of at most half hour on a topic related to the course but not taught (for instance, an application or the proof of a theorem);
- a final exam that consists in a group project or a seminar on the contend of a scientific publication;
some extra grades can be obtained through (non-mandatory):
- a simple laboratory test during the laboratory sessions (it might be substituted with some further lectures);
- the solution of some exercises given during the course.
Extended program
Least square approximation and singular value decomposition (principal component analysis).
QR factorization and Nonnegative matrix factorization. Matrices with positivity structure, eigenvalue computation. Non-linear optimization.
During the course, some applications to data science and information technologies will be taken into account: data fitting, complex networks; classification problems; machine learning.

Spline interpolation. B-splines. Trigonometric interpolation. Fast Fourier Transform. Application to digital filtering, curves and surfaces in computer graphics. Manifold optimization.
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