Publications by Daniel Kressner

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Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

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 ...

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...

A novel method for approximating structured singular values (also known as values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eigenvalue ...

The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form a ...

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

We examine a method for solving an infinite-dimensional tensor eigenvalue problem (Formula presented.), where the infinite-dimensional symmetric matrix (Formula presented.) exhibits a translational invariant structure. We provide a formulation of this type ...

This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is suffi ...

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 integral methods and preconditioned solvers such as the so-called locally opti ...

A result by Crouzeix and Palencia states that the spectral norm of a matrix function (Formula presented.) is bounded by (Formula presented.) times the maximum of f on (Formula presented.), the numerical range of A. The purpose of this work is to point out ...

A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or the trace of a symmetric positive semi-definite matrix. Several such probabilistic estimators have been pro ...

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

By the addition of entropic regularization, multimarginal optimal transport problems can be trans-formed into tensor scaling problems, which can be solved numerically using the multimarginal Sinkhorn algorithm. The main computational bottleneck of this alg ...

We consider linear systems A(alpha)x(alpha) - b(alpha) depending on possibly many parameters alpha = (alpha(1), ... , alpha(p)). Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort ...

We study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the coefficient. The resulting recursive deterministic pr ...

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time in ...

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this wor ...

Daniel Kressner

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Certified And Fast Computations With Shallow Covariance Kernels

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

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Chebyshev interpolation for nonlinear eigenvalue problems

A Novel Iterative Method To Approximate Structured Singular Values

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils

STREAMING TENSOR TRAIN APPROXIMATION

Solving a class of infinite-dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations

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

A bivariate extension of the Crouzeix–Palencia result with an application to Fréchet derivatives of matrix functions

Norm And Trace Estimation With Random Rank-One Vectors

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Truncated low-rank methods for solving general linear matrix equations

Low-Rank Tensor Approximations for Solving Multimarginal Optimal Transport Problems\ast

Low-rank tensor Krylov subspace methods for parametrized linear systems

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

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

Improved ParaDiag via low-rank updates and interpolation

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems