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

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

Systems of linear equations
* LU factorization and Gauss method
* Error analysis
* Iteration methods and their convergence
* Jacobi, Gauss-Seidel and Richardson methods

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