Constructive Approximation
A.Y. 2026/2027
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Objectives and problems of constructive approximation. Selected applications. Approximation using fixed partitions, adaptive partitions, and hierarchical partitions. Approximation using orthonormal bases. Fundamentals of approximation theory.
Prerequisites for admission
Essential: Analysis and Linear Algebra. Familiarity with MATLAB or a programming language, preferably C or C++.
Recommended: Familiarity with the Lebesgue integral.
Recommended: Familiarity with the Lebesgue integral.
Teaching methods
Lectures, exercise classes, and lab sessions held in person, except in special circumstances (e.g., strikes).
Teaching Resources
The course is based on selected material from
R. DeVore, Nonlinear Approximation, Acta Numerica (1998), 51-150.
R. DeVore, G. Lorentz, Constructive Approximation, Springer, 1993.
R. DeVore, Nonlinear Approximation, Acta Numerica (1998), 51-150.
R. DeVore, G. Lorentz, Constructive Approximation, Springer, 1993.
Assessment methods and Criteria
The examination consists of two parts:
1)the evaluation of a small project chosen from a given list; and
2) a final oral examination, held by individual appointment after enrollment in an appello (official examination session).
The project must be chosen from a list that will be published at the beginning of each examination session. The project may be completed in collaboration with one other student; however, all members of the group must complete the examination within the period of validity of the same project list.
The project must be submitted by email as a ZIP archive containing the source code (but no executable files, to avoid issues with antivirus software) and a PDF report describing the results in no more than five pages. Although the project may be completed collaboratively, student are advied to write their own report independently.
The ZIP archive, together with the name of the collaborator (if any), must be submitted by email at least two working days before the scheduled oral examination.
To arrange the date of the oral examination, the student must be enrolled in a current appello. Students are advised to contact the instructor at least one week before their preferred examination date. The oral examination usually begins with a brief discussion of the report and lasts approximately 45 minutes. Students should bring a copy of their report and be prepared to answer questions both related and unrelated to the chosen project. The examination cannot be repeated using the same project.
The examination is considered passed if both the report (including its discussion) and the oral examination are evaluated positively. Final grades are expressed on a scale from 0 to 30 and will be communicated at the end of the oral examination.
1)the evaluation of a small project chosen from a given list; and
2) a final oral examination, held by individual appointment after enrollment in an appello (official examination session).
The project must be chosen from a list that will be published at the beginning of each examination session. The project may be completed in collaboration with one other student; however, all members of the group must complete the examination within the period of validity of the same project list.
The project must be submitted by email as a ZIP archive containing the source code (but no executable files, to avoid issues with antivirus software) and a PDF report describing the results in no more than five pages. Although the project may be completed collaboratively, student are advied to write their own report independently.
The ZIP archive, together with the name of the collaborator (if any), must be submitted by email at least two working days before the scheduled oral examination.
To arrange the date of the oral examination, the student must be enrolled in a current appello. Students are advised to contact the instructor at least one week before their preferred examination date. The oral examination usually begins with a brief discussion of the report and lasts approximately 45 minutes. Students should bring a copy of their report and be prepared to answer questions both related and unrelated to the chosen project. The examination cannot be repeated using the same project.
The examination is considered passed if both the report (including its discussion) and the oral examination are evaluated positively. Final grades are expressed on a scale from 0 to 30 and will be communicated at the end of the oral examination.
MATH-05/A - Numerical Analysis - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professors:
Veeser Andreas, Zanotti Pietro
Professor(s)