2 citations · 5 across the 14 of their papers we have counts for
16 papers
Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation
Emmanuel Agullo, Hartwig Anzt, Daniel Bauer +37
Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accel…
Conditioning of solutions to the Sylvester equation
Massimiliano Fasi, Behnam Hashemi
We partially answer an open problem, posed by Nick Higham, concerning the conditioning of solutions to Sylvester and Lyapunov equations. The question arises in the backward stabili…
Probabilistic Error Analysis of Limited-Precision Stochastic Rounding: Horner's Algorithm and Pairwise Summation
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical…
What is New in Stochastic Rounding: a Survey on Theory, Hardware, and Applications
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length summation, the worst-case error of SR grow…
An Efficient Batch Solver for the Singular Value Decomposition on GPUs
Ahmad Abdelfattah, Massimiliano Fasi
The singular value decomposition (SVD) is a powerful tool in modern numerical linear algebra, which underpins computational methods such as principal component analysis (PCA), low-…
Exact quantum dynamics of Fermi--Hubbard systems using the Gaussian phase-space representation with diffusion gauges
F Rousse, M Fasi, A Dmytryshyn +3
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which re…
Computing matrix functions associated with a Hermitian-definite pencil
Dario A. Bini, Massimiliano Fasi, Bruno Iannazzo
We consider the numerical evaluation of the quantity , where is Hermitian positive definite, is Hermitian, and is a function defined on the spectrum of $A^…
Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Ahmad Abdelfattah, Jack Dongarra, Massimiliano Fasi +2
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer…
TypedMatrices.jl: An Extensible and Type-Based Matrix Collection for Julia
Anzhi Zhang, Massimiliano Fasi
TypedMatrices.jl is a Julia package to organize test matrices. By default, the package comes with a number of built-in matrices and interfaces to help users select test cases based…
Mixed-precision algorithms for solving the Sylvester matrix equation
Andrii Dmytryshyn, Massimiliano Fasi, Nicholas J. Higham +1
We consider the solution of the Sylvester equation in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations…
Probabilistic error analysis of limited-precision stochastic rounding
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms th…
Challenges in computing matrix functions
Massimiliano Fasi, Stéphane Gaudreault, Kathryn Lund +1
This manuscript summarizes the outcome of the focus groups at "The f(A)bulous workshop on matrix functions and exponential integrators", held at the Max Planck Institute for Dynami…
Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
F Rousse, M Fasi, A Dmytryshyn +2
The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical…
Computational graphs for matrix functions
Elias Jarlebring, Massimiliano Fasi, Emil Ringh
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly…
Sampling the eigenvalues of random orthogonal and unitary matrices
Massimiliano Fasi, Leonardo Robol
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samp…
A Backward/Forward Recovery Approach for the Preconditioned Conjugate Gradient Method
Massimiliano Fasi, Julien Langou, Yves Robert +1
Several recent papers have introduced a periodic verification mechanism to detect silent errors in iterative solvers. Chen [PPoPP'13, pp. 167--176] has shown how to combine such a…