| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| COMPUTER SCIENCE | ||
Course unit
NUMERICAL ANALYSIS
SC03100218, A.A. 2015/16
Information concerning the students who enrolled in A.Y. 2015/16
NUMERICAL ANALYSIS
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 COMPUTER SCIENCE SC1176, Degree course structure A.Y. 2014/15, A.Y. 2015/16 |
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|---|---|---|
| Number of ECTS credits allocated | 6.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | NUMERICAL ANALYSIS | |
| Website of the academic structure | http://informatica.scienze.unipd.it/2015/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | Italian | |
| Branch | PADOVA | |
| 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 |
Lecturers
| Teacher in charge | ALVISE SOMMARIVA | MAT/08 |
|---|
Mutuating
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| SCM0014413 | NUMERICAL ANALYSIS | ALVISE SOMMARIVA | SC1159 |
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 |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| 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. Eigenvalues. 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) |
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