Publications de Daniel Kressner

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The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...

This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation alg ...

A CUR approximation of a matrix A is a particular type of low-rank approximation A approximate to CUR, where C and R consist of columns and rows of A, respectively. One way to obtain such an approximation is to apply column subset selection to A and A(T). ...

In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a deterministic parame ...

This work considers the low-rank approximation of a matrix (Formula presented.) depending on a parameter (Formula presented.) in a compact set (Formula presented.). Application areas that give rise to such problems include computational statistics and dyna ...

This paper is concerned with low multilinear rank approximations to antisymmetric tensors, that is, multivariate arrays for which the entries change sign when permuting pairs of indices. We show which ranks can be attained by an antisymmetric tensor and di ...

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

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 ...

In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil , that is, A, B are Hermitian and there is a shift such that is definite. Our new meth ...

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

Markov chains that describe interacting subsystems suffer from state space explosion but lead to highly structured matrices. In this work, we propose a novel tensor-based algorithm to address such tensor-structured Markov chains. Our algorithm combines a t ...

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in root k, provided that the involved operator A gener ...

Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel multishift QR ...

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a MATLAB toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work ...

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 such matrices. Any Toeplitz matrix can be transformed into a matrix with of ...

Daniel Kressner

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A mixed precision LOBPCG algorithm

Bivariate Matrix Functions

Approximation in the extended functional tensor train format

Low-Rank Approximation In The Frobenius Norm By Column And Row Subset Selection

Multilevel tensor approximation of PDEs with random data

Randomized low-rank approximation of parameter-dependent matrices

Structure-Preserving Low Multilinear Rank Approximation Of Antisymmetric Tensors

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

From low-rank retractions to dynamical low-rank approximation and back

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

An indefinite variant of LOBPCG for definite matrix pencils

Functional Tucker Approximation Using Chebyshev Interpolation

Multigrid Methods Combined With Low-Rank Approximation For Tensor-Structured Markov Chains

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

On the eigenvalue decay of solutions to operator Lyapunov equations

Algorithm 953: Parallel Library Software for the Multishift QR Algorithm with Aggressive Early Deflation

Algorithm 941: htucker-A MATLAB Toolbox for Tensors in Hierarchical Tucker Format

Compression properties for large Toeplitz-like matrices

7th Workshop on Matrix Equations and Tensor Techniques