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| Corso | Ingegneria Elettrica ed Elettronica LM-29 |
| Curriculum | Electrical and Electronic Engineering |
| Orientamento | Orientamento unico |
| Anno Accademico | 2021/2022 |
| Crediti | 6 |
| Settore Scientifico Disciplinare | MAT/08 |
| Anno | Primo anno |
| Unità temporale | Primo semestre |
| Ore aula | 48 |
| Attività formativa | Attività formative affini ed integrative |
| Docente | MARIANTONIA COTRONEI |
| Obiettivi | The aim of the course is to provide basic knowledge about the main methods of numerical linear algebra, data approximation, numerical optimization and to introduce the Matlab scientific computing environment. The objectives of the course include the acquisition of: ability to build numerical models and to design solution algorithms; awareness of issues related to the use of computers for solving mathematical problems; ability to implement numerical algorithms on the computer, perform numerical tests and critically analyze the results obtained. |
| Programma | FLOATING-POINT ARITHMETICS AND ERROR ANALYSIS Representation of numbers. Numerical accuracy. Floating-point arithmetic. Errors and their propagation. Conditioning of a mathematical problem. Stability of an algorithm. SYSTEMS OF LINEAR EQUATIONS Stability analysis for linear systems. Condition number of a matrix. Direct methods. Resolution of triangular systems. Gaussian elimination. Pivoting. LU factorization. Iterative methods. Iteration matrix. Convergence and speed of convergence. Stop criteria. Jacobi and Gauss-Seidel methods. Richardson's and gradient methods. APPROXIMATION OF FUNCTIONS AND DATA Polynomial interpolation. Lagrange polynomial. Runge effect. Interpolation with spline functions. Linear and cubic splines. Trigonometric interpolation and FFT. Least squares approximation. Resolution of overdetermined systems. NUMERICAL OPTIMIZATION Unconstrained optimization. Methods for one-dimensional functions: bisection, Newton, dichotomic research, golden section, parabolic interpolation. Descent methods: gradient, Newton, quasi-Newton, conjugate gradient. Overview of constrained optimization methods. INTRODUCTION TO MATLAB Matlab scientific environment: main commands, arrays, mathematical functions, plots, programming. |
| Testi docente | A. Quarteroni, F. Saleri, P. Gervasio. Scientific Computing with MATLAB and Octave, Springer |
| Erogazione tradizionale | Sì |
| Erogazione a distanza | No |
| Frequenza obbligatoria | No |
| Valutazione prova scritta | Sì |
| Valutazione prova orale | Sì |
| Valutazione test attitudinale | No |
| Valutazione progetto | No |
| Valutazione tirocinio | No |
| Valutazione in itinere | No |
| Prova pratica | No |
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