Study-unit NUMERICAL APPROXIMATION WITH APPLICATIONS
Course name | Mathematics |
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Study-unit Code | A003061 |
Curriculum | Didattico-generale |
Lecturers |
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Hours |
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CFU | 6 |
Course Regulation | Coorte 2023 |
Supplied | 2024/25 |
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 | English or Italian (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. |