Floating point representation of numbers and round off errors. Conditioning of the problems and stability of the algorithms. Basic numerical methods for solving nonlinear equations and linear algebraic systems, polynomial interpolation, (composite) quadrature formulas. Basic notions of Matlab.
L. Brugnano, C. Magherini, A. Sestini, Calcolo Numerico, Masterbooks, 2019.
Learning Objectives - Last names A-K
Being able to write Matlab programming codes and use predefined functions. Knowledge of existing numerical methods for the problems discussed during the lectures and ability to choose the best one for solving a given problem. Being able to compare different methods based on theoretical properties and practice.
Prerequisites - Last names A-K
Mathemathics I (mandatory)
Teaching Methods - Last names A-K
Total number of lectures hours: 32
Total number of practice hours: 24
Type of Assessment - Last names A-K
The exam is an oral test which consists in questions related to the topics addressed by the course lectures and exercises.
Course program - Last names A-K
Introduction to algorithms and their main building components. Floating point representation of numbers and round off errors. Conditioning of the problem and stability of the algorithms. Basic
numerical methods for solving: nonlinear equations (bisection, Newton, quasi-Newton);
linear algebraic systems (Gauss method with and without pivot), conditioning of a linear system, error analysis, iterative methods (Jacobi and Gauss-Seidel); polynomial interpolation (Lagrange polynomial), interpolation error, conditioning of interpolation problem. Integration rules:
Trapezi and Simpson methods, composite quadrature formulas (Trapezoidal formula, Simpson formula, composite formulas). Basic notions of Matlab.