Publications by Daniel Kressner

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Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

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 ...

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well under ...

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...

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) structure. Appearing in a wide variety of applications, often in the context of ...

The Hadamard product features prominently in tensor-based algorithms in scientific computing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithms based on lo ...

Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper differs from Stewart's classical result and sometimes yields tighter bounds. Moreover, we provide norm estimates for t ...

The contragredient transformation A bar right arrow P-1 AP-(inverted perpendicular) , B bar right arrow P-inverted perpendicular BP of two matrices A, B effects simultaneous similarity transformations of the products AB and BA. This work provides structure ...

Given a Hilbert space H and a finite measure space Ω, the approximation of a vector-valued function f:Ω→H by a k-dimensional subspace U⊂H plays an important role in dimension reduction techniques, such as reduced basis methods for solving parameter-depende ...

In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques on the manifold of tensors of fixed multilinear rank. More spe ...

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 ...

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness fo ...

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 ...

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 ...

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Gal ...

We study differential equations that lead to extremal points in symplectic pseudospectra. In a two-level approach, where on the inner level we compute extremizers of the symplectic epsilon-pseudospectrum for a given epsilon and on the outer level we optimi ...

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modele ...

Daniel Kressner

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RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

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

Projection Methods For Large-Scale T-Sylvester Equations

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

COMPUTING FUNCTIONS OF SYMMETRIC HIERARCHICALLY SEMISEPARABLE MATRICES

Recompression Of Hadamard Products Of Tensors In Tucker Format

On A Perturbation Bound For Invariant Subspaces Of Matrices

Structured Canonical Forms For Products Of (Skew-) Symmetric Matrices And The Matrix Equation XAX = B

On the approximation of vector-valued functions by volume sampling

Low-rank tensor completion by Riemannian optimization

Randomized Low-Rank Approximation Of Monotone Matrix Functions

Generalized eigenvalue problems with specified eigenvalues

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Recursive blocked algorithms for linear systems with Kronecker product structure

Iterative refinement of Schur decompositions

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

An Error Analysis Of Galerkin Projection Methods For Linear Systems With Tensor Product Structure

Computing Extremal Points Of Symplectic Pseudospectra And Solving Symplectic Matrix Nearness Problems

Linearization techniques for band structure calculations in absorbing photonic crystals