Numerical analysis with laboratory (2014/2015)
Scientific Disciplinary Sector (SSD)
MAT/08 - NUMERICAL ANALYSIS
The teaching is organized as follows:
Implementation in Matlab and/or GNU Octave of the main algorithms of Numerical Analysis.
The basics of Numerical Analysis.
* Analysis of errors: Overflow, Underflow, Cancellation
* Nonlinear equations: the Bisection Method, Fixed Point Iterations, Newton's Method, the Secant Method, Polynomials, Horner's Rule
* Linear Systems: Direct Methods, the LU Decomposition and Pivoting, Forward and Back Substitution; Iterative Methods, Jacobi Iteration, Gauss-Seidel and SOR. Iterative Improvement, the Gradient Method, Conjugate Gradient, over and under determined systems
* Eigenvalues and Eigenvectors: the Power Method, the Inverse Power Method, the QR algorithm
* Interpolation and Approximation fo Functions and Data: Polynomial interpolation, the Newton and Lagrange forms. Splines. Least Squares and the SVD.
* Numerical Integration and Derivatives: Simple formulas for the estimation of a derivative with relative error, numerical quadrature, interpolatory formulas, composite formulas, Gaussian Quadrature, Adaptive Quadrature.
* Numerical Solution of ODE's (time permitting)
There will be an oral esam consisting of two parts. The first part will be a discussion of a selection of the assigned Laboratory exercises. The second part will be based on the theory presented during the lectures.
Students are asked to bring copies of the exercises and their solutions to the exam.
Attending the Laboratory and completing the assigned exercises are necessary conditions for passing the course.