Advanced numerical analysis (2017/2018)

Course code
4S001108
Name of lecturer
Leonard Peter Bos
Coordinator
Leonard Peter Bos
Number of ECTS credits allocated
6
Academic sector
MAT/08 - NUMERICAL ANALYSIS
Language of instruction
English
Period
I sem. dal Oct 2, 2017 al Jan 31, 2018.

Lesson timetable

Go to lesson schedule

Learning outcomes

The course will discuss the theory and practice of approximation of functions and data, in both the univariate and multivariate setting, with an emphasis on splines of various types and interpolation. A part of the course will be held in a Laboratory setting where some of the techniques presented during the lectures will be implemented in Matlab. At the end of the course the student is expected to able to demonstrate an in-depth knowledge of the techniques of univariate and multivariate approximation.

Syllabus

Programme:

Hermite-Genocchi formula
Peano Kernel formula
Univariate splines of degrees 0, 1 and 3.
Haar Wavelets
Cubic Smoothing splines
Subdivision of spline curves and surfaces
General Univariate Spline spaces
Thin Plate Splines in 2 dimensions
RBF interpolation and positive definite functions
The Theorems of Bochner, Schoenberg and Micchelli

Reference books
Author Title Publisher Year ISBN Note
C. de Boor A Practical Guide to Splines (Edizione 1) Springer 1978
L. Bos Course Notes 2017 Available online

Assessment methods and criteria

The purpose of the exam is to see if the student is able to recall and reproduce the theory and practice of interpolation and approximation, both univariate and multivariate. The exam will be oral.

STUDENT MODULE EVALUATION - 2017/2018