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Daniel Kressner

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Publications associées (97)

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

Daniel Kressner, Alice Cortinovis

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). ...

SIAM PUBLICATIONS2020

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

Daniel Kressner, Francesco Statti, Kathrin Beatrice Glau

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. ...

2020

Numerical Mathematics and Control Preface to a Special Issue Dedicated to Volker Mehrmann on the Occasion of his 65th Birthday

Daniel Kressner

SPRINGER SINGAPORE PTE LTD2020

Certified And Fast Computations With Shallow Covariance Kernels

Daniel Kressner, Stefano Massei

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 ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

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 ...

SPRINGER2020

hm-toolbox: Matlab software for HODLR and HSS matrices

Daniel Kressner, Stefano Massei

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 ...

2019

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

Daniel Kressner, Stefano Massei

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 ...

SIAM PUBLICATIONS2019

Distributed Signal Processing via Chebyshev Polynomial Approximation

Pascal Frossard, Pierre Vandergheynst, David Shuman, Daniel Kressner

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of ...

2018

FAST COMPUTATION OF THE MATRIX EXPONENTIAL FOR A TOEPLITZ MATRIX

Daniel Kressner, Robert Gerhard Jérôme Luce

2018

LOW-RANK UPDATES OF MATRIX FUNCTIONS

Daniel Kressner, Marcel Schweitzer

2018

SUBSPACE ACCELERATION FOR THE CRAWFORD NUMBER AND RELATED EIGENVALUE OPTIMIZATION PROBLEMS

Daniel Kressner

2018

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

Daniel Kressner, Francisco Santos Paredes Quartin de Macedo

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 ...

2018

7th Workshop on Matrix Equations and Tensor Techniques

Daniel Kressner

WILEY2018

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Daniel Kressner, Zvonimir Bujanovic

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 ...

SIAM PUBLICATIONS2018

Structure-Preserving Low Multilinear Rank Approximation Of Antisymmetric Tensors

Daniel Kressner

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 ...

Siam Publications2017

Recompression Of Hadamard Products Of Tensors In Tucker Format

Daniel Kressner, Lana Perisa

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 ...

Siam Publications2017

A Novel Iterative Method To Approximate Structured Singular Values

Daniel Kressner

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 ...

Siam Publications2017

Multilevel tensor approximation of PDEs with random data

Daniel Kressner, Jonas Ballani, Michael Dieter Peters

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 ...

Springer2017

Fast Computation Of Spectral Projectors Of Banded Matrices

Daniel Kressner, Ana Susnjara

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...

Siam Publications2017

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

Daniel Kressner, Michael Maximilian Steinlechner

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 ...

Siam Publications2016

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