ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| METODI DI APPROSSIMAZIONE/a | MAT/08 | LEZIONI | 42 |
|
Il corso si concentra su tecniche avanzate di algebra lineare numerica e le sue applicazioni. Lo studente che completa il corso sarà a conoscenza di diversi argomenti di algebra lineare numerica sviluppati recentemente, e avrà una descrizione dello stato della ricerca in questi campi.
Quest'anno il corso si concentrerà su funzioni di matrici ed equazioni matriciali tipo-Riccati (inclusa qualche applicazione alla teoria dei controlli).
This course focuses on advanced techniques in numerical linear algebra (NLA) and their applications. The student who successfully completes the course will be aware of several contemporary topics in numerical linear algebra. The student will be also able to have a look at the state of the local research in these fields.
This year the course will cover matrix functions and Riccati-type matrix equations (with some applications to control theory).
(si veda la versione inglese del programma per informazioni dettagliate.)
The final exam is based on a seminar: the students will need to read, understand, and repeat the numerical experiments (to some extent) of a research paper in numerical linear algebra (to be agreed with the teacher), and make a short presentation on it.
Possibly, if the number of students allows it, a shorter lecture on a smaller topic will be assigned during the course.
(si veda la versione inglese del programma per informazioni dettagliate.)
Students will see some modern techniques and problems in numerical linear algebra and be able to interface themselves with contemporary papers, numerical experiments, and research presentations.
(si veda la versione inglese del programma per informazioni dettagliate.)
During the course and the final exam.
(si veda la versione inglese del programma per informazioni dettagliate.)
Students will learn to choose the most effective numerical algorithms for a variety of NLA problems related to matrix functions and equations. They will acquire awareness on their strengths and weaknesses in terms of accuracy and stability.
(si veda la versione inglese del programma per informazioni dettagliate.)
During the final exam, by checking the ability to perform adequate numerical experimentation.
(si veda la versione inglese del programma per informazioni dettagliate.)
The material covered in our undergraduate courses on numerical analysis and numerical linear algebra (including the program of the undergraduate/graduate course *Calcolo Scientifico* taught at Unipi); a solid command of linear algebra and proof-based mathematics. Some experience with programming (and numerical programming), to implement and test the algorithms encountered. Working knowledge of the English language (if the course is taught in English).
(si veda la versione inglese del programma per informazioni dettagliate.)
Delivery: frontal lectures with coding examples in Matlab (either in-person or online, Khan-style using a tablet).
Learning activities:
Attendance: Not mandatory
Teaching methods:
(si veda la versione inglese del programma per informazioni dettagliate.)
(tentative) Kronecker products and Sylvester equations. Introduction to matrix functions and equations. Conditioning and Fréchet derivatives. Numerical methods for generic and special matrix functions (exponential, sign function, square root). Introduction to control theory (linear time-invariant systems, controllability criteria). Lyapunov and Riccati equations: solvability properties and numerical methods (Newton, matrix sign iteration, and a brief outline of methods for sparse equations).
(si veda la versione inglese del programma per informazioni dettagliate.)
N. Higham, Functions of matrices.
B. Datta, Numerical Methods for Linear Control Theory.
A good research textbook to fill in on the standard algorithms is Golub, Van Loan, Matrix computations, 4th edition.
(si veda la versione inglese del programma per informazioni dettagliate.)
The lectures will be recorded (barring technical issues), so it is expected that even non-attending students can follow them. Non-attending students are expected to get familiar with the material covered in the course, and to contact the teacher to agree a topic for the final presentation.
(si veda la versione inglese del programma per informazioni dettagliate.)
Oral exam, with a presentation on a research topic decided beforehand in agreement with the teacher.
The course page will be created on Moodle https://elearning.dm.unipi.it/ .
The course page will be created on Moodle https://elearning.dm.unipi.it/ .
