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. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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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/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
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

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
INP5070471 MESH FREE APPROXIMATIONS OF PARTIAL DIFFERENTIAL EQUATIONS STEFANO DE MARCHI IN2191

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

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Laboratory 1.0 8 17.0 No turn
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

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)

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 the use of polynomials and radial basis functions. Applications: interpolation, hyoerinterpolation, quadrature and solution of PDEs. 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 (24h+2h): from univariate to multivariate 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 (24h+6h): Radial Basis Functions (RBF)
- learning from splines
- positive and conditionally definite functions
- native spaces, power function and error estimates
- application to the solution of elliptic PDEs
- applications and lab (10h)
Planned learning activities and teaching methods: The course consists of 48h of frontal teaching lessons and 8h of lab exercises.
Additional notes about suggested reading: - For PART I: teacher's lecture notes(see below)
- For PART II: lectures notes of the teacher and the reference books.
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
  • Wen Chen, Zhuo-Ja Fu and C.S. Chen, Recent Advances in Radial Basis Function Collocation Methods. --: Springer (Briefs in Applied Sciences and Tech.), 2014. Cerca nel catalogo