Learning objectives

The course will discuss, from both the analytic and computational points of view, the numerical solution of Mathematical problems such as: non linear systems, linear systems, matrix eigenvalues, interpolation and approximation, Gaussian quadrature. The objective therefore is to expand on the material introduced in Calcolo Numerico I and to introduce new and more sophisticated solution algorithms. In particular, we will present techniques that are fundamental for important modern problems of Applied Mathematics such as that of high dimensional datasets (SVD and PCoA) and optimization (conjugate gradient method). The course has a Laboratory component where the methods studied will be implemented using the MATLAB programming platform (using either the official Matlab from Mathworks or else the open source version GNU OCTAVE). At the end of the course the student will be expected to demonstrate that s/he has attained a level of competence in the computational and computer aspects of the course subject, as well as the ability to recognize which algorithms are appropriate for basic and advanced problems of numerical analysis.