|
Course unit
THEORY OF APPROXIMATION AND APPLICATIONS
SCN1037767, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
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 |
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)
|
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.
-
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.
|
|
|