Publications by Daniel Kressner

Recursive blocked algorithms for linear systems with Kronecker product structure

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

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

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

MATHICSE Technical Report : 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 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 its transpose. In this work, ...

MATHICSE2019

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a

k\times k

submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...

MATHICSE2019

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

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

Daniel Kressner, Stefano Massei

In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic proc ...

MATHICSE2019

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

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325{A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we c ...

MATHICSE2018

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

Daniel Kressner

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Recursive blocked algorithms for linear systems with Kronecker product structure

Certified And Fast Computations With Shallow Covariance Kernels

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

MATHICSE Technical Report : Low-rank approximation in the Frobenius norm by column and row subset selection

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

hm-toolbox: Matlab software for HODLR and HSS matrices

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

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

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

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

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

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

Recursive blocked algorithms for linear systems with Kronecker product structure

MATHICSE Technical Report : Low-rank approximation in the Frobenius norm by column and row subset selection

Certified And Fast Computations With Shallow Covariance Kernels

hm-toolbox: Matlab software for HODLR and HSS matrices

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations