
Bachelor

Master

PhD
Courses

Lie Groups and Algebras

Numerical Method for Graphics

Krylov Methods and Applications

Game Theory

Algorithms and Data Structures

Scientific Computing

Programming Languages

Computational Lab

Schemes

Elements of Computational Algebra

Optimization

Groups and Representations

Elements of Algebraic Geometry

Code Theory and Cryptography

Neural Networks
Thesis
Courses
Didactics
Bachelor Thesis :
Supervisor: Dario Andrea Bini
Date: 19/09/2014
Doctoral Thesis :
Theory and ApplicationDriven Structure
Supervisors: Stefano SerraCapizzano, Michele Benzi
Date: 10/02/2020
Master Thesis :
Theory with an application to translations invariant image processing
Supervisors: Luca Gemignani, Francesco Romani
Date: 14/10/2016
Lie Groups and Algebras Course 2018:
 Notes: Pdf [ENG]
Numerical Method for Graphics Course 2018:
 Notes: Pdf [ENG]
Krylov Methods and Applications Course 2018:
 Notes: Pdf [ENG]
Game Theory Course 2018:
 Notes: Pdf [ITA]
Algorithms and Data Structure Course :
Scientific Computing :
 Relation on Lars Eldén , 2002, Partial leastsquares vs. Lanczos BidiagonalizationI: analysis of a projection method for multiple regression: PDF [ITA]
 Experiments on PLS, PCR, LBD and Conjugated Gradient: Slides [ITA]
 Octave functions used: Zip [ITA]
Programming Languages Course :
 A Fully Abstract Model of PCF, in collaboration with Gianluca Grilletti: Slides [ITA]
Computational Lab :
 Maximal Biclique Extraction Problem: PDF [ENG]
Schemes Course 2015:
 Notes [ITA]
Elements of Computational Algebra Course 2015:
 Notes of the course, main author Carlo Sircana: Notes [ITA]
 Jacobi Symbol and its computation: PDF [ENG]
 Programs used for the computation of Jacobi Symbol: Zip
Optimization Course :
Groups and Representations Course 2016:
 Notes of the course: PDF [ITA]
Elements of Algebraic Geometry Course 2016:
 Notes of the course, main authors Riccardo Morandin, Viola Siconolfi: Notes [ITA]
Code Theory and Cryptography Course 2016:
 Notes of the course, in collaboration with Riccardo Morandin, Carlo Sircana: Notes [ITA]
 ReedMuller Code and decoding: PDF [ITA]
Neural Network :
 Simple C++ Interface for Neural Networks: Zip [ENG]

Articles

Conferences
Articles
Conferences
Research
My main interests are the asymptotic spectral analysis of matrices and the lowrank factorization of matrices.
I have worked on matrix sequences coming from the discretization of linear PDE,
on random matrix polynomial with growing size and/or degree, on perturbation of Hermitian matrices,
and on matrices utilized in iterative methods.
Moreover, I worked in community detection, clustering and predition problems
through the lens of lowrank factorization methods, with a focus in nonnegative matrix factorization.
Supported by the ERC consolidator grant no 101085607 of the European Union (Sep 2023  Jun 2026)
Project: Beyond LowRank Factorizations (eLinoR)
Articles, Preprints and Notes:

Barbarino G., Cicone A.
Stabilization and Variations to the Adaptive Local Iterative Filtering Algorithm: the Fast Resampled Iterative Filtering Method
Numerische Mathematik (Jan 2024)  Online  PDF 
Barbarino G., Garoni C.
Normal form for GLT sequences, functions of normal GLT sequences, and spectral distribution of perturbed normal matrices
Arxiv (Jan 2024) 
Barbarino G.,
Ekström S.E.,
Garoni C.,
Meadon D.,
SerraCapizzano S.,
Vassalos P.
Spectral properties of flipped Toeplitz matrices
(Dec 2023). 
Barbarino G.,
On the Periodicity of Singular Vectors and the Holomorphic BlockCirculant SVD on the Unit Circumference
Arxiv (Dec 2023). 
Barbarino G., Cavassi R.,
Cicone A.
Extension and convergence analysis of Iterative Filtering to spherical data
Arxiv (Dec 2023). 
Barbarino G.,
Pestana J.,
Proudler I.,
Weiss S.
Properties and Structure of the Analytic Singular Value Decomposition
(Sep 2023). 
Barbarino G.,
Ekström S.E.,
Garoni C.,
Meadon D.,
SerraCapizzano S.,
Vassalos P.
From asymptotic distribution and vague convergence to uniform convergence, with numerical applications
Arxiv (Sep 2023). 
Barbarino G., Noferini V.
On the Rellich eigendecomposition of paraHermitian matrices and the sign characteristics of ∗palindromic matrix polynomials
Linear Algebra and its Applications 672, 127 (Sep 2023)  PDF 
Barbarino G.
Ergodic Estimations for Toeplitz Sequences Generated by a Symbol
Arxiv (Aug 2023). 
Barbarino G.,
Garoni C.
An extension of the theory of GLT sequences: sampling on asymptotically uniform grids
Linear and Multilinear Algebra 71, 12, pp. 20082025 (Aug 2023)  PDF 
Barbarino G., Noferini V.,
Van Dooren P.
On role extraction for digraphs via neighbourhood pattern similarity
Physical Review E 106 (5), 054301 (Nov 2022)  PDF 
Barbarino G., Cicone A.
Conjectures on spectral properties of ALIF algorithm
Linear Algebra and Its Applications, 647, pp. 127–152 (Aug 2022)  PDF 
Barbarino G.,
Ekström S.E.,
SerraCapizzano S.,
Vassalos P.
Theoretical results for eigenvalues, singular values, and eigenvectors of (flipped) Toeplitz matrices and related computational proposals
Arxiv (Jul 2022). 
Barbarino G., Noferini V.
The limit empirical spectral distribution of complex matrix polynomials
Random Matrices: Theory and Applications 11, 3 (Jul 2022)  PDF 
Barbarino G., Garoni C.,
Mazza M.,
SerraCapizzano S.
Rectangular GLT sequences
Electronic Transactions on Numerical Analysis. Volume 55, pp. 585–617. (Jun 2022)  PDF 
Barbarino G.,
Bianchi D.,
Garoni C.
Constructive approach to the monotone rearrangement of functions
Expositiones Mathematicae 40, 1 (Mar 2022) 155175  PDF 
Barbarino G., Noferini V.
The limit empirical spectral distribution of Gaussian monic complex matrix polynomials
Journal of Theoretical Probability, (Feb 2022)  PDF 
Barbarino G.
A systematic approach to reduced GLT
Bit Numer Math 62, 3 (Sep 2021) 681743  PDF 
Barbarino G.,
Claesson M.,
Ekström S.E.,
Garoni C.,
Meadon D.,
Matrixless eigensolver for large structured matrices
Technical Report, Uppsala University (Aug 2021) 
Barbarino G., SerraCapizzano S.
Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations
Numer Linear Algebra Appl. 2020;e2286 (Mar 2020)  PDF 
Barbarino G., Garoni C., SerraCapizzano S.
Block Generalized Locally Toeplitz Sequences: Theory and Applications in the Multidimensional Case
Electronic transactions on numerical analysis ETNA 53:1 (Jan 2020)  PDF 
Barbarino G., Garoni C., SerraCapizzano S.
Block Generalized Locally Toeplitz Sequences: Theory and Applications in the Unidimensional Case
Electronic transactions on numerical analysis ETNA 53:1 (Jan 2020)  PDF 
Barbarino G.
Spectral Measures
Structured Matrices in Numerical Linear Algebra. Springer INdAM Series, vol 30 (Apr 2019)  PDF 
Barbarino G.
Notes on asymptotic eigenvalues distribution on complex circles
Arxiv (2018) 
Barbarino G.
Conjectures on Perturbations of Hermitian Sequences
Arxiv (2018) 
Barbarino G.
Diagonal Matrix Sequences and their Spectral Symbols
Arxiv (2017) 
Barbarino G., Garoni C.
From convergence in measure to convergence of matrixsequences through concave functions and singular values
Electr. J. Linear Algebra 32 (2017) 500513  PDF 
Barbarino G.
Equivalence between GLT sequences and measurable functions
Linear Algebra Appl. 529 (2017) 397412  PDF 
Barbarino G.
Permutation NMF
Arxiv (2016)
Conferences, Summer Schools and Presentations
 XXII Congresso dell’Unione Matematica Italiana (Sep 2023  Pisa)
The Fast Resampled Iterative Filtering Method  Invited Speaker at Foundations of Computational Mathematics FoCM (Jun 2023  Paris)
Role Extraction for Digraphs via Neighbourhood Pattern Similarity  ILAS LAA Early Career Award, Early Career Speakers at 25th Conference of the International Linear Algebra Society (Jun 2023  Madrid)
On the eigendecomposition of paraHermitian matrices  Invited Speaker at Mathematics for Signal processing and Applications in Geophysics and other fields MaSAG23 (May 2023  Rome)
New stability results for IF Methods  Numerical Linear Algebra Days (May 2023  L'Aquila)
Reduced GLT and Applications  SEminar on Linear algebra and Operator Theory OSELOT (Feb 2023  Online)
On the Rellich eigendecomposition of paraHermitian matrices on the unit circle [Video ENG]  ALAMA 2022  ALN2gg (Jun 2022  Alcalá de Henares)
Approximation of the LaplaceBeltrami operator by its symbol [ENG]  NNLA 2022 (Apr 2022  Helsinki)
The limit empirical spectral distribution of complex matrix polynomials [ENG]
 Invited Speaker  NoSAG 21 (Lug 2021  L'Aquila)
Iterative Filtering Algorithms [Video ENG no commentary]
Slides [ENG]  CommNLA (Nov 2020  Online)
The limit empirical spectral distribution of complex matrix polynomials [Video ENG] Youtube Link  Staff Meeting (Oct 2019  Helsinki)
Symbols for matrixsequences: ApplicationDriven Structure [ENG] 
Two days of Linear Algebra and Applications (Feb 2019  Rome)

Intelligent Machines and Mathematics (Jan 2019  Bologna)

Parallel Scientific Computing Exam (Winter 2018)
Higher order spectral symbols and eigenvalues approximation for Toeplitz matrices [ENG]  GNCS Indam Assembly (Feb 2018  Montecatini)

Two days of Linear Algebra and Applications (Feb 2018  Padua)
Perturbations of Hermitian Matrices and Applications to Spectral Symbols [ENG]  Como Talks (Oct 2017)
Generalized Locally Toeplitz Sequences: a Link between Measurable Functions and Spectral Symbols [ENG]
Ordering the Eigenvalues: GLT Symbols and Spectral Measures [ENG] 
INdAM Meeting
Structured Matrices in Numerical Linear Algebra:
Analysis, Algorithms and Applications (Sept 2017  Cortona)
Equivalence between GLT sequences and measurable functions [ENG] 
CIMEEMS Summer School on Splines and PDEs (July 2017  Cetraro)
Equivalence between GLT sequences and measurable functions [ENG]  Two days of Linear Algebra (Feb 2017  Como)
 RomeMoscow Summer School (Summer 2016)
Permutation NMF [ENG]  MidTerm at SNS (Spring 2015)
QuasiBirth and Death Stochastic Processes with an infinite number of phases: asymptotic decay properties [ITA]
About
2023  now : PostDoctoral Researcher at
UMONS in Numerical Analysis
2020  2023 : PostDoctoral Researcher at
Aalto University in Numerical Analysis
2016  2020 : Ph.D. Degree at SNS in Mathematics
2014  2016 : Master Degree at Pisa University and SNS in Applied Mathematics
2011  2014 : Three Year Bachelor Degree at Pisa University and SNS in Mathematics
Member of GNCS Indam ( Scientific Computing National Group )
Member of SIAM Activity Group on Linear Algebra (SIAG/LA)
Member of ILAS International Linear Algebra Society
Reviewer at ZbMATH ( Zentralblatt MATH ), MR ( Mathematical Reviews  MathSciNet ), and for scientific journals:
 Applied Mathematics and Computation
 Journal of Mathematics
 Mathematical Methods in the Applied Sciences
 BIT Numerical Mathematics
 SIAM Journal on Matrix Analysis and Applications (SIMAX)
 Applied and Computational Harmonic Analysis
 Linear and Multilinear Algebra
 Electronic Journal of Linear Algebra
Researcher at:
Interests:
 Applied Math
 Computer Science
 C/C++/Python
 Artificial Intelligence
Other:
 Latex
 QtCreator
 HTML/css
 Wordpress
Other
Partecipant and Organizer of Italian Mathematical Olympiad. Some useful Links: Oliforum: official forum of Italian Mathematical Olympiad [ITA]
 Vid: official videolessons of stages [ITA]
 IMO: International Mathematical Olympiad website [ENG]
 AoPS: Forum, Tutorials, Lessons and much more on Mathematics and Mathematical Olympiad [ENG]
 MateMate: blog on notsoelementary problems [ITA]
 AndFog: collection of problems and interesting mathematical facts [ITA]
Chess Program for Terminal: Executable
Left Chess for Browser (under development): Website
Rischiatutto Department Edition, presented by Bargagnati
Other info in the origin.