First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
COMPLEMENTS OF NUMERICAL ANALYSIS
SCP3051015, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination COMPLEMENTS OF NUMERICAL ANALYSIS
Website of the academic structure http://matematica.scienze.unipd.it/2015/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 CLAUDE BREZINSKI

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 3.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 01/10/2015
End of activities 28/01/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
3 Complementi di Analisi Numerica - a.a. 2016/2017 01/10/2016 31/12/2017 BREZINSKI CLAUDE (Presidente)
REDIVO ZAGLIA MICHELA (Membro Effettivo)
MARTINEZ CALOMARDO ANGELES (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
TUDISCO FRANCESCO (Supplente)
2 Complementi di Analisi Numerica - a.a. 2015/2016 01/10/2015 30/09/2016 BREZINSKI CLAUDE (Presidente)
REDIVO ZAGLIA MICHELA (Membro Effettivo)
DE MARCHI STEFANO (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
VIANELLO MARCO (Supplente)

Syllabus
Prerequisites: The course requires a basic knowledge of calculus, linear algebra and numerical analysis.
Target skills and knowledge: The aim of the courses is to introduce Master students to some recent research subjects in numerical analysis (especially those related to approximation and numerical linear algebra) and
to provide them the theoretical basis for their understanding. Applications will also be discussed.
Examination methods: The final exam will be a written test on the topics of the course or a small research project.
Assessment criteria: The students will have to show that they master the topics of the course, both from the theoretical and algorithmic point of view.
Course unit contents: Course unit contents:
The various topics developed at different levels will be
1. Formal orthogonal polynomials
- Definition
- Algebraic properties
- Recurrence relation
- Adjacent Families
2. Padé approximation
- Definition and algebraic properties
- Padé-type approximants
- Connection to formal orthogonal polynomials
- Recursive computation
- Connection to continued fractions
- Some elements of convergence theory
- Applications
3. Krylov subspace methods
- Definition
- Lanczos method
- Recurrence relations
- Implementation
4. Extrapolation methods
- Sequence transformations and convergence acceleration
- What is an extrapolation method?
- Various extrapolation methods
- Vector sequence transformations
- Applications
i. Treatment of the Gibbs phenomenon
ii. Web search
iii. Estimation of the error for linear systems
iv. Regularization of linear systems
v. Estimation of the trace of matrix powers
vi. Acceleration of Kaczmarz method
vii. Fixed point iterations
viii. Computation of matrix functions
Planned learning activities and teaching methods: The course consists of 48h of lessons.
Additional notes about suggested reading: Lecture notes will be provided to the students.
Textbooks (and optional supplementary readings)
  • Brezinski, Claude, Pade-Type Approximation and General Orthogonal PolynomialsC. Brezinski. Basel: Birkhauser, 1980.
  • Brezinski, Claude; Redivo Zaglia, Michela, Extrapolation methodstheory and practiceClaude Brezinski, Michela Redivo Zaglia. Amsterdam <etc.>: North-Holland, 1991.
  • C. Brezinski, Projection Methods for Systems of Equations. --: North-Holland, Amsterdam, 1997.