Stefano Sicilia

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20222026

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6 papers · 1 filter

math.NA2026

Structured distance to singularity as a nonlinear system of equations

Miryam Gnazzo, Nicola Guglielmi, Federico Poloni +1

In this article we study the structured distance to singularity for a nonsingular matrix $A \in C^{n \times n}$ , with a prescribed linear structure $S$ (for instanc…

math.NA2025

Improving the robustness of neural ODEs with minimal weight perturbation

Arturo De Marinis, Nicola Guglielmi, Stefano Sicilia +1

We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initia…

math.NA2024

Minimum-norm solutions of the non-symmetric semidefinite Procrustes problem

Nicolas Gillis, Stefano Sicilia

Given two matrices $X, B \in R^{n \times m}$ and a set $A \subseteq R^{n \times n}$ , a Procrustes problem consists in finding a matrix $A \in A$ su…

math.NA2024

Stabilization of a matrix via a low rank-adaptive ODE

Nicola Guglielmi, Stefano Sicilia

Let $A$ be a square matrix with a given structure (e.g. real matrix, sparsity pattern, Toeplitz structure, etc.) and assume that it is unstable, i.e. at least one of its eigenvalue…

math.NA2023

A low rank ODE for spectral clustering stability

Nicola Guglielmi, Stefano Sicilia

Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W \in R^{n \times n}$ by exploiting its graph Laplacian…

math.NA2022

Rank- $1$ matrix differential equations for structured eigenvalue optimization

Nicola Guglielmi, Christian Lubich, Stefano Sicilia

A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to comput…