First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
THEORY OF APPROXIMATION AND APPLICATIONS
SCN1037767, 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
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination THEORY OF APPROXIMATION AND APPLICATIONS
Website of the academic structure http://matematica.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 STEFANO DE MARCHI MAT/08

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/08 Numerical Analysis 3.0
Core courses MAT/08 Numerical Analysis 4.0

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

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Laboratory 1.0 16 9.0 No turn
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 01/10/2015
End of activities 28/01/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
4 Teoria dell'Approssimazione e Applicazioni - 2017/2018 01/10/2017 30/09/2018 DE MARCHI STEFANO (Presidente)
VIANELLO MARCO (Membro Effettivo)
MARCUZZI FABIO (Supplente)
MARTINEZ CALOMARDO ANGELES (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
3 Teoria dell'Approssimazione e Applicazioni - 2016/2017 01/10/2016 30/11/2017 DE MARCHI STEFANO (Presidente)
KROO ANDRAS (Membro Effettivo)
MARCUZZI FABIO (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
VIANELLO MARCO (Supplente)
2 Teoria dell'Approssimazione e Applicazioni - a.a. 2015/2016 01/10/2015 30/09/2016 DE MARCHI STEFANO (Presidente)
SOMMARIVA ALVISE (Membro Effettivo)
MARCUZZI FABIO (Supplente)
PUTTI MARIO (Supplente)
VIANELLO MARCO (Supplente)

Syllabus
Prerequisites: The course requires the basic courses of Numerical Calculus and Numerical Analysis. It is also useful to have attended a course of Functional Analysis. It is assumed that the students know the programming language Matlab.
Target skills and knowledge: Analysis of some approximation problems in 1-dimension and more dimensions, with use of polynomials and radial basi functions. Applications to interpolation and quadrature. Error analysis. Solution of test problems by the use of Matlab.
Examination methods: The final exam is a written test on the topics of the course. There will be also an oral part in which the student will discuss the lab exercises given during the course.
Assessment criteria: The student will have to show that he has understood the topics of the course, both from the theoretical and algorithmic point of view, either on the application point of view.
During the lab, it will be important to show familiarity and confidence on the use of Matlab.
Course unit contents: The course can be subdvided in 2 theoretical parts of 24h each, in total 48h corresponding to 6CFU. Moreover there will be 16h of lab exercises.

PART I (20h+6h): polynomial approximation
- best approximation approximation
- modulus of continuity and Lebesgue constant
- nearly optimal distribution of points in 1-dimension
- Padua points for interpolation and cubature
- (Weakly) admissible meshes
- applications and lab (6h)

PART II (28h+10h): Radial Basis Functions (RBF)
- learning from splines
- positive definite functions
- conditionally positive definite functions
- error estimates
- applications and lab (10h)
Planned learning activities and teaching methods: The course consists of 48h of frontal teaching lessons and 16h of lab exercises.
Additional notes about suggested reading: - For PART I: teacher's lecture notes(see below)
- For PART II: see the reference book by G. Fasshauer and the some lectures notes of the teachers.
Textbooks (and optional supplementary readings)
  • Gregory E. Fasshauer, Meshfree Approximation Methods with Matlab. --: World Scientific Publishing Co., 2008. Cerca nel catalogo
  • Stefano De Marchi, Lectures on Multivariate Polynomial Interpolation. --: --, 2015. Lectures notes
  • Stefano De Marchi, Four lectures on Radial Basis Functions. --: --, 2014. Lectures notes