D. Bini, M. Capovani, O. Menchi. Metodi Numerici per l'algebra lineare,Zanichelli, 1988.
M.G. Gasparo, Metodi Numerici per il cacolo di autovalori ed autovettori, valori singolari e vettori singolari di matrcii reali. Dispense
G. Monegato, Fondamenti di calcolo numerico, CLUT Editore, 1998.
A. Quateroni, R. Sacco, F. Saleri, Matematica Numerica, Springer, 2000.
Learning Objectives
To be able to solve more sofisticated numerical problems also with the help of Matlab
Prerequisites
Basic of numerical analysis, Linear algebra and Calculus
Teaching Methods
Lectures and laboratory training
Type of Assessment
Oral exame including teh writing of a simple Matlab code
Course program
Numerical Methods for eigenvectors and eigenvalues: general ideas. Localization theorems ad conditioning of the problem. Reduction to the Hessemberg form via orthogonal transformation. Givens and Householder matrices. Numerical methods for symmetric tridiagonal matrices. The Sturm method. The power method and its variants. The orthogonal iteration method and the QR method.
Singular value decomposition (SVD). Position of the problem. Existence and uniqueness of the SVD. SVD and low rank approximations.
SVD and condition number. SVD and pseudo inverse of a matrix. Rectangular linear systems: the solution of ordinary least squares problem via SVD.
Numerical methods for initial value problems. The Chauchy problem. General ideas on numerical methods. One step method. Runge Kutta methods and Runge-Kutta Fehlberg methods; Automatic algorithms for numerical integration.
Matlab for the solution of several problems in the mentioned domains.