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Bachelor
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Master
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PhD
Courses
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Topics in Low Rank Factorization and Data Analysis
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Lie Groups and Algebras
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Numerical Method for Graphics
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Krylov Methods and Applications
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Game Theory
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Algorithms and Data Structures
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Scientific Computing
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Programming Languages
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Computational Lab
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Schemes
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Elements of Computational Algebra
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Optimization
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Groups and Representations
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Elements of Algebraic Geometry
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Code Theory and Cryptography
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Neural Networks
Thesis
Courses
Didactics
Bachelor Thesis :
Supervisor: Dario Andrea Bini
Date: 19/09/2014
Doctoral Thesis :
Theory and Application-Driven Structure
Supervisors: Stefano Serra-Capizzano, 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
Topics in Low Rank Factorization and Data Analysis Course 2024:
- PCA
- Clustering
- Clustering
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 least-squares vs. Lanczos Bidiagonalization-I: 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 Bi-clique 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]
- Reed-Muller Code and decoding: PDF [ITA]
Neural Network :
- Simple C++ Interface for Neural Networks: Zip [ENG]
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Articles
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Conferences
Articles
Conferences
Research
My main interests are the asymptotic spectral analysis of matrices and the low-rank 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 low-rank 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 Low-Rank Factorizations (eLinoR)
Articles, Preprints and Notes:
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Barbarino G., Cavassi R.,
Cicone A.
Extension and convergence analysis of Iterative Filtering to spherical data
Linear Algebra and its Applications, in press (Jun 2024) - PDF -
Barbarino G.,
McWhirter J.G.,
Pestana J.,
Proudler I.,
Weiss S.
On Properties and Structure of the Analytic Singular Value Decomposition
IEEE Transactions on Signal Processing 72, pp. 2260-2275 (Apr 2024). -
Abdolali M.,
Barbarino G., Gillis N.
Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization
Arxiv (Mar 2024) -
Barbarino G.,
On the Periodicity of Singular Vectors and the Holomorphic Block-Circulant SVD on the Unit Circumference
Linear Algebra and its Applications, in press (Mar 2024) - PDF -
Barbarino G., Cicone A.
Stabilization and Variations to the Adaptive Local Iterative Filtering Algorithm: the Fast Resampled Iterative Filtering Method
Numerische Mathematik 156, 395-433 (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.,
Serra-Capizzano S.,
Vassalos P.
Spectral properties of flipped Toeplitz matrices
(Dec 2023). -
Barbarino G.,
Ekström S.-E.,
Garoni C.,
Meadon D.,
Serra-Capizzano 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 para-Hermitian matrices and the sign characteristics of ∗-palindromic matrix polynomials
Linear Algebra and its Applications 672, 1-27 (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. 2008-2025 (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.,
Serra-Capizzano 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.,
Serra-Capizzano 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, pp. 155-175 (Mar 2022) - 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) 681--743 - PDF -
Barbarino G.,
Claesson M.,
Ekström S.-E.,
Garoni C.,
Meadon D.,
Matrix-less eigensolver for large structured matrices
Technical Report, Uppsala University (Aug 2021) -
Barbarino G., Serra-Capizzano 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., Serra-Capizzano 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., Serra-Capizzano 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 matrix-sequences through concave functions and singular values
Electr. J. Linear Algebra 32 (2017) 500--513 - PDF -
Barbarino G.
Equivalence between GLT sequences and measurable functions
Linear Algebra Appl. 529 (2017) 397--412 - PDF -
Barbarino G.
Permutation NMF
Arxiv (2016)
Conferences, Summer Schools and Presentations
- 8th Alama Meeting: Linear Algebra, Matrix Analysis and Applications (Jun 2024 - Gijón)
Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization [ENG] - SIAM Conference on Applied Linear Algebra LA24 (May 2024 - Paris)
Ergodic Estimations for Toeplitz Sequences [ENG] - 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 [ENG] - ILAS LAA Early Career Award, Early Career Speakers at 25th Conference of the International Linear Algebra Society (Jun 2023 - Madrid)
On the eigendecomposition of para-Hermitian 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 [ENG] - SEminar on Linear algebra and Operator Theory OSELOT (Feb 2023 - Online)
On the Rellich eigendecomposition of para-Hermitian matrices on the unit circle [Video ENG] - ALAMA 2022 - ALN2gg (Jun 2022 - Alcalá de Henares)
Approximation of the Laplace-Beltrami 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 matrix-sequences: Application-Driven Structure [ENG] -
Two days of Linear Algebra and Applications (Feb 2019 - Rome)
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Intelligent Machines and Mathematics (Jan 2019 - Bologna)
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Parallel Scientific Computing Exam (Winter 2018)
Higher order spectral symbols and eigenvalues approximation for Toeplitz matrices [ENG] - GNCS Indam Assembly (Feb 2018 - Montecatini)
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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] -
CIME-EMS 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)
- Rome-Moscow Summer School (Summer 2016)
Permutation NMF [ENG] - Mid-Term at SNS (Spring 2015)
Quasi-Birth and Death Stochastic Processes with an infinite number of phases: asymptotic decay properties [ITA]
About
2023 - now : Post-Doctoral Researcher at
UMONS in Numerical Analysis
2020 - 2023 : Post-Doctoral 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 video-lessons 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 not-so-elementary 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.