Study-unit NUMERICAL APPROXIMATION WITH APPLICATIONS
| Course name | Mathematics |
|---|---|
| Study-unit Code | A003061 |
| Curriculum | Didattico-generale |
| Lecturer | Bruno Iannazzo |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2023/24 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | 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 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. |
| Prerequisites | |
| Teaching methods | Face-to-face lectures and laboratory sessions, using Matlab/Octave |
| Other information | |
| Learning verification modality | Oral exam and seminar. The oral exam can be substituted by some exercises, a project or a seminar, upon availability. |
| Extended program | Least square approximation and singular value decomposition (principal component analysis). QR factorization and Nonnegative matrix factorization. Eigenvalue computation. Non-linear and manifold optimization. During the course, some applications to data science and information technologies will be taken into account: data fitting, classification problems; machine learning. Spline interpolation. B-splines. Trigonometric interpolation. Fast Fourier Transform. Application to digital filtering, curves and surfaces in computer graphics. |