Publications associées à Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Ulf David Persson, Alice Cortinovis

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2021

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Felix Schürmann, Bruno Ricardo Da Cunha Magalhães

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of row ...

2020

Charge fluctuations from molecular simulations in the constant-potential ensemble

Sara Bonella, Alessandro Coretti

We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the c ...

2020

A Computational Framework For Two-Dimensional Random Walks With Restarts

Stefano Massei

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 low-rank correction. We propose an extension of the framework introduced in ...

SIAM PUBLICATIONS2020

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Kathryn Dianne Lund

We analyze an expansion of the generalized block Krylov subspace framework of [Electron.\ Trans.\ Numer.\ Anal., 47 (2017), pp. 100-126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and con ...

MATHICSE2019

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Volkan Cevher, Yen-Huan Li

Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...

2018

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

,

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

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Optimal denoising of rotationally invariant rectangular matrices

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Charge fluctuations from molecular simulations in the constant-potential ensemble

A Computational Framework For Two-Dimensional Random Walks With Restarts

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Convergence of the Exponentiated Gradient Method with Armijo Line Search

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Charge fluctuations from molecular simulations in the constant-potential ensemble

Efficient Learning of a Linear Dynamical System with Stability Guarantees

A Computational Framework For Two-Dimensional Random Walks With Restarts

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Optimal denoising of rotationally invariant rectangular matrices