Portale di Ateneo - En.Unibs.it

Programming with Matlab
* Scalar variables and arrays
* Arithmetic operations and operations with arrays
* Functions and graphical elements
* Branching and loops

Computer arithmetic
* Number representation
* Floating point number systems
* Rounding error
* Arithmetic in floating point number systems and error propagation

Solution of linear systems of equations
* LU factorization and Gauss method
* Choleski factorization
* Error analysis
* Condition number

Iteration methods for the solution of linear systems of equation
* Classical iteration methods and convergence analysis
* Stopping criteria
* Jacobi, Gauss-Seidel and Richardson methods
* Conjugate gradient
* Preconditioning

Eigenvalue problems
* Introductory remarks
* Localization of eigenvalues
* Eigenvalues and eigenvectors of symmetric positive definte matrices
* Power methods
* Rayleigh quotient
* QR algorithm

Nonlinear systems of equations
* Bisection method
* Newton and secant methods
* Extension to the solution of nonlinear systems
* Convergence analysis

Optimization
* Unconstrained optimization
* Newton and line-search method

Approximation of functions and data
* Interpolation by polynomials
* The interpolation error
* Spline functions
* Least square methods for data approximation

Numerical differentiation and integration
* Numerical integration
* Quadrature by interpolation formulas
* Adaptive Simpson formula
* Finite differences

Ordinary differential equations
* The Cauchy problem
* Euler and Cranc-Nicolson methods
* Theory for one-step methods
* Absolute stability region
* High order methods
* Systems of ordinary differential equations

Numerical methods for boundary value problems
* Finite differences approximation of boundary value problems for
stationary partial differential equations
* Finite differences approximation of time dependent problems
* Finite element method
* Discretization of Laplace equation, heat equation and wave equation