Gaussian Quadrature, Iterative Methods and Applications

Prof. Alessandro Buccini, Prof. Caterina Fenu, Prof. Luisa Fermo, Prof. Giuseppe Rodriguez

Università degli Studi di Cagliari

Abstract

A Gaussian quadrature rule is optimal, i.e., it integrates exactly a polynomial of degree 2n-1 using n function evaluations, and it does not exist a formula with a higher algebraic precision. Recently, a strong relation has been outlined which connects Gauss quadrature to the Lanczos process and other Krylov projection methods. Such properties allow the construction of iterative methods for specific large scale problems, which produce both an approximate solution and an error estimate. During the course, a complete introduction to this topic will be given, and various applications will be discussed in the fields of complex network analysis and inverse problems. During laboratory sessions, instructors will assist the students in the implementation of the algorithms presented.

To attend the classes, students should possess a solid understanding of master level topics in linear algebra and numerical analysis, as well as some experience in Matlab programming.

Schedule

The course will last 22 hours in total. The first class will be held on July 7 and 10, 2026, from 9.00 to 12.00.  Subsequent classes will be planned with participants.
Classes will be held exclusively in presence.

Exam

Students who need a final assessment will have to prepare a written paper on selected topics covered in the course, as agreed upon with the instructors. The paper must contain both a theoretical discussion and the results of numerical experiments.

Enrolment

Interested students are requested to contact, as soon as possible, Giuseppe Rodriguez <rodriguez@unica.it>