28 citations · 68 across the 25 of their papers we have counts for
30 papers
Computing the density of the Kesten-Stigum limit in supercritical Galton-Watson processes
Alice Cortinovis, Sophie Hautphenne, Stefano Massei
This paper proposes a novel numerical method for computing the density of the limit random variable associated with a supercritical Galton-Watson process. This random variable capt…
Error formulas for block rational Krylov approximations of matrix functions
Stefano Massei, Leonardo Robol
This paper investigates explicit expressions for the error associated with the block rational Krylov approximation of matrix functions. Two formulas are proposed, both derived from…
On the data-sparsity of the solution of Riccati equations with applications to feedback control
Stefano Massei, Luca Saluzzi
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coeff…
Optimal Polynomial Smoothers for Parallel AMG
Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone +2
In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These acce…
AdamL: A fast adaptive gradient method incorporating loss function
Lu Xia, Stefano Massei
Adaptive first-order optimizers are fundamental tools in deep learning, although they may suffer from poor generalization due to the nonuniform gradient scaling. In this work, we p…
Optimizing network robustness via Krylov subspaces
Stefano Massei, Francesco Tudisco
We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weig…
On the Convergence of the Gradient Descent Method with Stochastic Fixed-point Rounding Errors under the Polyak-Lojasiewicz Inequality
Lu Xia, Michiel E. Hochstenbach, Stefano Massei
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study…
A nested divide-and-conquer method for tensor Sylvester equations with positive definite hierarchically semiseparable coefficients
Stefano Massei, Leonardo Robol
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional opera…
Improved ParaDiag via low-rank updates and interpolation
Daniel Kressner, Stefano Massei, Junli Zhu
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equati…
On the influence of stochastic roundoff errors and their bias on the convergence of the gradient descent method with low-precision floating-point computation
Lu Xia, Stefano Massei, Michiel E. Hochstenbach +1
When implementing the gradient descent method in low precision, the employment of stochastic rounding schemes helps to prevent stagnation of convergence caused by the vanishing gra…
Divide and conquer methods for functions of matrices with banded or hierarchical low-rank structure
Alice Cortinovis, Daniel Kressner, Stefano Massei
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer m…
Hierarchical adaptive low-rank format with applications to discretized PDEs
Stefano Massei, Leonardo Robol, Daniel Kressner
A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approxima…
Mixed precision recursive block diagonalization for bivariate functions of matrices
Stefano Massei, Leonardo Robol
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fréchet derivative along a direction, th…
Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices
Stefano Massei
Finding the submatrix of maximum volume of a matrix is an NP hard problem that arises in a variety of applications. We propose a new greedy…
Compress-and-restart block Krylov subspace methods for Sylvester matrix equations
Daniel Kressner, Kathryn Lund, Stefano Massei +1
Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, e.g., from the discretization of part…
A computational framework for two-dimensional random walks with restarts
Dario A. Bini, Stefano Massei, Beatrice Meini +1
The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a…
hm-toolbox: Matlab software for HODLR and HSS matrices
Stefano Massei, Leonardo Robol, Daniel Kressner
Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While e…
Rational Krylov for Stieltjes matrix functions: convergence and pole selection
Stefano Massei, Leonardo Robol
Evaluating the action of a matrix function on a vector, that is , is an ubiquitous task in applications. When is large, one usually relies on Krylov…
Low-rank updates and divide-and-conquer methods for quadratic matrix equations
Daniel Kressner, Patrick Kürschner, Stefano Massei
In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control,…
On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices
Alice Cortinovis, Daniel Kressner, Stefano Massei
The problem of finding a submatrix of maximum volume of a matrix is of interest in a variety of applications. For example, it yields a quasi-best low-rank approxim…
A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes
Sophie Hautphenne, Stefano Massei
We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton--Watson branching processes. This algorithm is based on a particular discretization…
Fast solvers for two-dimensional fractional diffusion equations using rank structured matrices
Stefano Massei, Mariarosa Mazza, Leonardo Robol
We consider the discretization of time-space diffusion equations with fractional derivatives in space and either 1D or 2D spatial domains. The use of implicit Euler scheme in time…
Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
Dario A. Bini, Stefano Massei, Leonardo Robol
A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind where , is compact and the norms…
Low-rank updates and a divide-and-conquer method for linear matrix equations
Daniel Kressner, Stefano Massei, Leonardo Robol
Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction…