Publications related to DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

A fast spectral divide-and-conquer method for banded matrices

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

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

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Daniel Kressner, Alice Cortinovis

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

2021

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

2020

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

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 existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Marius Christopher Lemm

The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel ...

2020

Sub-Matrix Factorization for Real-Time Vote Prediction

Patrick Thiran, Matthias Grossglauser, Victor Kristof

We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, effic ...

2020

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

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

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A fast spectral divide-and-conquer method for banded matrices

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Efficient Learning of a Linear Dynamical System with Stability Guarantees

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Recursive blocked algorithms for linear systems with Kronecker product structure

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Sub-Matrix Factorization for Real-Time Vote Prediction

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

A fast spectral divide-and-conquer method for banded matrices

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Recursive blocked algorithms for linear systems with Kronecker product structure

Sub-Matrix Factorization for Real-Time Vote Prediction

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants