Constructive Approximation

A.Y. 2020/2021
Overall hours
Learning objectives
To present the main algorithms for approximating a known function and to provide an introduction to the analysis for their convergence speed.
Expected learning outcomes
The ability to judge and to apply the main algorithms for approximating a known function.
Course syllabus and organization

Single session

Lesson period
Second semester
Assessment methods and critera for its result
The assessment methods and critera for its results will not been changed, except for the fact that the final oral exam will be in person or on Microsoft Teams according to the existing directives in force at the time of the exam.

Course structure
The course will employ the platform Ariel for announcements and providing material. Lectures, exercises and lab sessions will be organized on Microsoft Teams (or Zoom) and can be followed according to the timetable or by means of recordings that will be available on Microsoft Teams (or Ariel).

The course syllabus will not be changed.
Course syllabus
Some fundamental examples of approximation and applications.
Best and near-best approximation.
Approximation with piecewise polynomials, orthonormal bases and wavelets.
Function spaces and fundamental theorems of approximation.
Prerequisites for admission
Essential: Analysis and Linear Algebra. Matlab or some programming language, preferable C or C++.
Useful: Lebesgue integral.
Teaching methods
Lectures, exercises and lab sessions.
Teaching Resources
The course is based on a choice of material from

R. DeVore, Nonlinear approximation, Acta Numerica (1998), 51-150.
R. DeVore, G. Lorentz, Constructive Approximation, Spinger, 1993.
Assessment methods and Criteria
The examination consists of two parts:
- the evaluation of a small project to be chosen and
- a final oral exam on personal appointment after enrollment in an "appello".

The project has to be chosen from a list that will be published at the the beginning of each exam session. The project can be realized in collaboration with another person; each member of the group has to complete its exam within the validity of the given project list. The correct submission of the project consists in a zip archive containing source codes (but no exectuable files for the antivirus) and a pdf report which summarizes the obtained results on at most 5 pages; it is recommended to write the report not in collaboration. The zip archive, together with the name of the collaborator (if present), has to be sent by email two workdays before the oral exam.

In order to arrange the date of the oral exam, the student has to be enrolled in the current "appello"; it is recommended to contact the professor at least one week before the desired date. Usually, the oral exam starts with a brief discussion on the report and lasts 45 minutes. The student is invited to present a copy of its report and to prepare for questions both concerning or not the chosen project. The exam cannot be repeated with the same project.

The examination is passed if the report and its discussion are evaluated positively and the oral exam is successfully passed. Final marks are given using the numerical range 0-30, and will be communicated after the oral examination.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
on appointment by email
Skype or Microsoft Teams