First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
STATISTICS AND INFORMATION TECHNOLOGIES
Course unit
NUMERICAL ANALYSIS (LABORATORY)
SSM0014101, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2013/14

Information on the course unit
Degree course First cycle degree in
STATISTICS AND INFORMATION TECHNOLOGIES
SS1451, Degree course structure A.Y. 2009/10, A.Y. 2015/16
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Degree course track METODOLOGICO [001PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS (LABORATORY)
Website of the academic structure http://www.stat.unipd.it/risorse/STI
Department of reference Department of Statistical Sciences
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 MARCO VIANELLO MAT/08
Other lecturers FABIO MARCUZZI MAT/08

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SCN1032583 NUMERICAL COMPUTING AND PROGRAMMING MARCO VIANELLO SC1173

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/08 Numerical Analysis 8.0

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Laboratory 2.0 16 34.0 No turn
Lecture 6.0 40 110.0 No turn

Calendar
Start of activities 30/09/2015
End of activities 23/01/2016
Show course schedule 2015/16 Reg.2009 weekly timetable
2015/16 Reg.2009 single teaching timetable

Examination board
Board From To Members of the board
5 Commissione Calcolo Numerico e Programmazione 18-19 01/10/2018 30/11/2019 DE MARCHI STEFANO (Presidente)
MARCUZZI FABIO (Membro Effettivo)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
4 Commissione Calcolo Numerico e Programmazione 17-18 01/10/2017 30/09/2018 VIANELLO MARCO (Presidente)
MARCUZZI FABIO (Membro Effettivo)
SOMMARIVA ALVISE (Supplente)
3 Commissione Calcolo Numerico e Programmazione 16-17 01/10/2016 30/09/2017 VIANELLO MARCO (Presidente)
MARCUZZI FABIO (Membro Effettivo)
SOMMARIVA ALVISE (Supplente)
2 Commissione Calcolo Numerico e Programmazione 15-16 01/10/2015 30/09/2016 VIANELLO MARCO (Presidente)
MARCUZZI FABIO (Membro Effettivo)

Syllabus
Prerequisites: Mathematical analysis 1 and 2

Linear algebra and geometry
Target skills and knowledge: Learning numerical computing fundamentals in view of scientific and technological applications, with special attention to the concepts of error, discretization, approximation, convergence, stability, computational cost
Examination methods: Oral exam
Course unit contents: Floating-point sistem and error propagation

Numerical solution of nonlinear equations

Interpolation and approximation of functions and data

Numerical integration and differentiation

Elements of numerical linear algebra

Introduction to finite difference methods for differential equations
Planned learning activities and teaching methods: Floating-point system and error propagation:
truncation and rounding error, floating-point representation of reals, machine precision, operations with approximate numbers, conditioning of functions, error propagation in iterative algorithms, the concept of stability

Numerical solution of nonlinear equations:
bisection method, error estimate by the weigthd residual; Newton method, global convergence, convergence rate, local convergence, error estimate, other linearization methods; fixed-point iterations

Interpolation abd approximation of functions and data:
polynomial interpolation, Lagrange interpolation, interpolation error, the convergence problem (Runge's counterexample), Chebyshev interpolation, stability of interpolation; piecewise polynomial interpolation, spline interpolation; least-squares polynomial approximation

Numerical integration and differentiation:
algebraic and composite formulas, convergence and stability, examples; instability of differentiation, computing derivatives by difference formulas; the concept of extrapolation

Elements of numerical linear algebra:
vector and matrix norms, conditioning of matrices and systems; direct methods: Gaussian elimination method and LU factorization, computing the inverse matrix, QR factorization, least-squares method for overdetermined systems; iterative methods: Jacobi and Gauss-Seidel methods, general structure of stationary iterations, preconditioning; power method for the computation of extremal eigenvalues

Introduction to finite difference methods for differential equations:
explicit and implicit Euler method, trapezoidal method, convergence and stability, stiff systems; 1d and 2d Poisson equation; method of lines for the heat equation

Laboratory: implementation and application of numerical codes in Matlab
Additional notes about suggested reading: one of the suggested textbooks and online notes of the lecturer (www.math.unipd.it/~marcov/studenti.html)
Textbooks (and optional supplementary readings)
  • A. Quarteroni, F. Saleri, Introduzione al calcolo scientifico. --: Springer, --. Cerca nel catalogo
  • A. Quarteroni, F. Saleri, Scientific computing with Matlab and Octave. --: Springer, --. for Erasmus students Cerca nel catalogo
  • G. Rodriguez, Algoritmi numerici. --: Pitagora, --. Cerca nel catalogo