Related papers: Metodi Iterativi per Sistemi Lineari
This text grew up from the notes of a graduate course I gave at the University of Roma ``Tor Vergata'' in the academic year 2018--19. The subject is the classification of complex algebraic surfaces following Mori's theory. It includes the…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed by solving global optimization problems, which could be…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…
These are notes for the course CS-172 I first taught in the Fall 1986 at UC Berkeley and subsequently at Boston University. The goal was to introduce the undergraduates to basic concepts of Theory of Computation and to provoke their…
An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve…
This volume contains the papers presented at LINEARITY 2014, the Third International Workshop on Linearity, held on July 13, 2014 in Vienna, Austria. The workshop was a one-day satellite event of FLoC 2014, the sixth Federated Logic…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
In this article, we present an overview of different a posteriori error analysis and postprocessing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising inelectronic structure calculations for the calculation of…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie point symmetries, and their generalizations to the study of…
Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
Italian master's thesis in Computer Science. It is an overview of the standard tecniques developed in the field of Proof Theory, ending with some results in the new field of Deep Inference, plus an original contribution trying to relate…
The paper presents a comparative analysis of iterative numerical methods of Jacobi and Gauss-Seidel for solving systems of linear algebraic equations (SLAEs) with complex and real matrices. The ranges of convergence for both methods for…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
These are lecture notes of a course that I gave to people doing research for their Ph.D. thesis in theoretical chemistry or spectroscopy. The course was given on December 9-13, 2002, in Han-sur-Lesse, Belgium. The lecture notes start with…