Daniel Kressner

Stochastic trace estimation for positive trace-class operators

Zvonimir Bujanović, Luka Grubišić, Daniel Kressner +1

Implicit trace estimation aims to approximate the trace of a matrix or linear operator accessible only through matrix-vector or operator-vector products. In the matrix setting, the…

stat.ML2026

Stochastic trace estimation with tensor train random vectors

Zvonimir Bujanović, Daniel Kressner, Hrvoje Olić

Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured sett…

Kernel-based linear system identification using augmented Krylov subspaces

Fabio Matti, Martin Skovgaard Andersen, Tianshi Chen +1

We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's…

Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop

Noah Amsel, Yves Baumann, Paul Beckman +33

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…

A novel Krylov subspace method for approximating Fréchet derivatives of large-scale matrix functions

Daniel Kressner, Peter Oehme

We present a novel Krylov subspace method for approximating $L_f(A, E) \vc{b}$, the matrix-vector product of the Fréchet derivative $L_{f} (A, E)$ of a large-scale matrix function $f(…

Restoring similarity in randomized Krylov methods with applications to eigenvalue problems and matrix functions

Laura Grigori, Daniel Kressner, Nian Shao +1

The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard…

RJD-BASE: Multi-Modal Spectral Clustering via Randomized Joint Diagonalization

Haoze He, Artemis Pados, Daniel Kressner

We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonal…

On the randomized SVD in infinite dimensions

Daniel Kressner, David Persson, André Uschmajew

Randomized methods, such as the randomized SVD (singular value decomposition) and Nyström approximation, are an effective way to compute low-rank approximations of large matrices.…

Lanczos with compression for symmetric matrix Lyapunov equations

Angelo A. Casulli, Francesco Hrobat, Daniel Kressner

This work considers large-scale Lyapunov matrix equations of the form $A X + X A = c c^{T}$ , where $A$ is a symmetric positive definite matrix and $\boldsymbol…

Stochastic trace estimation for parameter-dependent matrices applied to spectral density approximation

Fabio Matti, Haoze He, Daniel Kressner +1

Stochastic trace estimation is a well-established tool for approximating the trace of a large symmetric matrix $B$ . Several applications involve a matrix that depends…

Compression Properties for large Toeplitz-like matrices

Bernhard Beckermann, Daniel Kressner, Heather Wilber

Toeplitz matrices are abundant in computational mathematics, and there is a rich literature on the development of fast and superfast algorithms for solving linear systems involving…

A preconditioned inverse iteration with an improved convergence guarantee

Foivos Alimisis, Daniel Kressner, Nian Shao +1

Preconditioned eigenvalue solvers offer the possibility to incorporate preconditioners for the solution of large-scale eigenvalue problems, as they arise from the discretization of…

Adaptive randomized pivoting for column subset selection, DEIM, and low-rank approximation

Alice Cortinovis, Daniel Kressner

We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can…

math.NA2024★ 1 cited

Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding

Haoze He, Daniel Kressner, Bor Plestenjak

It is well known that a family of $n \times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular…

Preconditioned Low-Rank Riemannian Optimization for Symmetric Positive Definite Linear Matrix Equations

Ivan Bioli, Daniel Kressner, Leonardo Robol

This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\t…

On a randomized small-block Lanczos method for large-scale null space computations

Daniel Kressner, Nian Shao

Computing the null space of a large sparse matrix $A$ is a challenging computational problem, especially if the nullity -- the dimension of the null space -- is not small. When app…

Subspace embedding with random Khatri-Rao products and its application to eigensolvers

Zvonimir Bujanović, Luka Grubišić, Daniel Kressner +1

Various iterative eigenvalue solvers have been developed to compute parts of the spectrum for a large sparse matrix, including the power method, Krylov subspace methods, contour in…

A simple, randomized algorithm for diagonalizing normal matrices

Haoze He, Daniel Kressner

We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the…

Randomized Nyström approximation of non-negative self-adjoint operators

David Persson, Nicolas Boullé, Daniel Kressner

The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and stro…

Computing Functions of Symmetric Hierarchically Semiseparable Matrices

Angelo A. Casulli, Daniel Kressner, Leonardo Robol

The aim of this work is to develop a fast algorithm for approximating the matrix function $f (A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS)…