Publications de Ulf David Persson

Near-optimal hierarchical matrix approximation from matrix-vector products

We describe a randomized algorithm for producing a near-optimal hierarchical off-diagonal low-rank (HODLR) approximation to an n × n matrix A, accessible only though matrix-vector products with A and AT. We prove that, for the rank-k HODLR approximation pr ...

Society for Industrial and Applied Mathematics2025

ALGORITHM-AGNOSTIC LOW-RANK APPROXIMATION OF OPERATOR MONOTONE MATRIX FUNCTIONS

Ulf David Persson

Low-rank approximation of a matrix function, f(A), is an important task in computational mathematics. Most methods require direct access to f(A), which is often considerably more expensive than accessing A. Persson and Kressner [SIAM J. Matrix Anal., 44 (2 ...

2025

Randomized low-rank approximation and its applications

Ulf David Persson

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

Randomized Low-Rank Approximation Of Monotone Matrix Functions

Daniel Kressner, Ulf David Persson

This work is concerned with computing low-rank approximations of a matrix function f(A) for a large symmetric positive semidefinite matrix A, a task that arises in, e.g., statistical learning and inverse problems. The application of popular randomized meth ...

SIAM PUBLICATIONS2023

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