Algorithms. Floating point arithmetic. Conditioning and stability. Direct methods for linear systems. NUmerical methos for the zeros of a function. Interpolation and approximation.
M.G. Gasparo, R. Morandi, Elementi di Calcolo Numerico: metodi ed algoritmi, McGraw-Hill, 2008
Learning Objectives
To know numerical methods for linear systems, non linear equations, approximation. Capability of writing simple algorithms. Basic knowledge of the package Matlab.
Prerequisites
Linear algebra and Calcolus
Teaching Methods
Frontal lessons and Matlab exercises in lab.
Type of Assessment
written exam to verify the skill of solving a simple basic problem of numerical analysis. Oral discussion about it
Course program
Algorithms. Floating point arithmetics. Finite precision. Norms of matrices and vectors.
Conditioning of a problem.
Stability of an algorithm. Direct methods for linear systems: Gauss method and pivoting strategies. Jacobi and Gauss-Siedel iterative methods for linear systems.
Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; corresponding algorithms.
MATLAB: Handling matrices, operations between matrices. Function and script files.
If, while and for commands.
2D e 3D plots. Built-in functions for linear systems, nonlinear equations, basic fitting.