Portale di Ateneo - En.Unibs.it

Basic methods of scientific computing.
Floating point arithmetics and rounding errors.
Basic instructions in MATLAB and Octave.
Linear systems: LU, Cholesky, and QR factorizations. Errors analysis: condition number, stability of algorithms. Iterative methods: Jacobi, Gauss-seidel. Conjugate Gradient methods.
Non-linear equations and systems: Bisection, secant and Newton methods for scalar equations. Newton for systems.
Approximation of both functions and data: Lagrange interpolation (simple and composite). Spline. Interpolation errors. Linear least squares.
Numeric integration: simple and composite quadrature formulas. Errors analysis.
Approximation of initial value problems: forward and backward Euler, Crank-Nicolson schemes. Convergence, consistency, stability. Absolute stability. Runge-Kutta and multistep methods. Predictor-corrector methods. Examples of stiff problems.