Concept
Décomposition d'une matrice en éléments propres
Publications associées (223)
RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...
Philadelphia2024High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...
2024Preconditioning techniques for generalized Sylvester matrix equations
Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they recently arose in stochastic Galerkin finite element discretizations and isogeometric analysis. In th ...
2023Singular quadratic eigenvalue problems: linearization and weak condition numbers
Daniel Kressner, Ivana Sain Glibic
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...
SPRINGER2023Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...
AMER PHYSICAL SOC2023Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces
We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...
OXFORD UNIV PRESS2023The first Grushin eigenvalue on cartesian product domains
Joachim Stubbe, Luigi Provenzano, Paolo Luzzini
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
WALTER DE GRUYTER GMBH2023A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication
David Atienza Alonso, Giovanni Ansaloni, Grégoire Axel Eggermann, Marco Antonio Rios
State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...
2023