The course introduces some of the main techniques for the solution of numerical problems that find widespread use in fields like data analysis, machine learning, and artificial intelligence. These techniques often combine concepts typical of numerical analysis with those proper of numerical optimization, since numerical analysis tools are essential to solve optimization problems, and, vice-versa, problems of numerical analysis can be solved by optimization algorithms. The course has a significant hands-on part whereby students learn how to use some of the most common tools for computational mathematics; during these sessions, specific applications will be briefly illustrated in fields like regression and parameter estimation in statistics, approximation and data fitting, machine learning, artificial intelligence, data mining, information retrieval, and others.
- Multivariate and matrix calculus
- Matrix factorization, decomposition and approximation
- Eigenvalue computation
- Nonlinear optimization: theory and algorithms
- Least-squares problems and data fitting
- MATLAB and other software tools (lab sessions with applications)