First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC03100218, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
SC1176, Degree course structure A.Y. 2014/15, A.Y. 2015/16
bring this page
with you
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ALVISE SOMMARIVA MAT/08

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/08 Numerical Analysis 6.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Start of activities 01/03/2016
End of activities 15/06/2016
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Examination board not defined

Target skills and knowledge: Advanced knowledge of Numerical Analysis and its applications in Applied Mathematics.
Examination methods: Classroom and computer labs lessons.
Assessment criteria: Oral exam.
Course unit contents: Interpolation.
Orthogonal polynomials.
Numerical quadrature.
Iterative methods for linear algebra.
Nonlinear systems.
Finite differences methods for ODEs and PDEs.
Planned learning activities and teaching methods: Interpolation.
The general problem of interpolation, unisolvent sets and determinantal formula of Lagrange, the univariate and multivariate case, Lebesgue constant, fundamental estimate for interpolation error, stability, brief introduction to tensorial product interpolation and Fekete points.

Orthogonal polynomials.
Orthogonalization of the monomial basis, three-terms recurrence, the theorem of the zeros, classical orthogonal polynomials, Chebyshev polynomials.

Numerical quadrature.
Algebraic and composite rules, Gaussian rules, Polya-Steklov theorem, stability, Stieltjes theorem, brief introduction to product rules.

Numerical linear algebra.
Fundamental theorem of matrix inversion and applications (Gershgorin theorem of eigenvalues localization), iterative methods for linear systems, successive approximation theorem, preconditioning, gradient method, step and residual stop criteria, methods for the computation of eigenvalues and eigenvectors, Rayleigh quotient, power method and variants, QR method.

Numerical nonlinear algebra.
Solution of nonlinear systems of equations, fixed point iterations and Banach theorem, convergence estimates and stability, Newton method, local convergence and speed of convergence, step criterion, Newton method as fixed point iteration.

Finite difference methods for ODEs and PDEs.
Initial value problem: Euler method (explicit and implicit), convergence and stability in the Lipschitzian and dissipative case, trapezoidal method (Crank-Nicolson), stiff problems, conditional and unconditional stability; boundary problems: finite difference methods for the Poisson equations in 1D and 2D, structure of the linear system and convergence, computational issues; the lines method for the heat equation in the 1D and 2D case, relationships with the stiff problems.
Textbooks (and optional supplementary readings)
  • A. Quarteroni e F. Saleri, Introduzione al Calcolo scientifico. Esercizi e problemi risolti con Matlab.. --: Springer, 2004. Cerca nel catalogo
  • K. Atkinson and W. Han, Elementary Numerical Analysis. --: Wiley, 2003.