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Daniel Kressner

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Publications associées (97)

Projection Methods For Large-Scale T-Sylvester Equations

Daniel Kressner

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 ...

Amer Mathematical Soc2016

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

Daniel Kressner, Jonas Ballani

We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rbTensor, consists of three ingredients. ...

Siam Publications2016

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

Daniel Kressner, Petar Sirkovic

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix A(mu) for many parameter values mu in a domain D subset of R-P. The design of reliable and efficient algorithms for addressing this task is of impor ...

Siam Publications2016

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

Daniel Kressner, André Uschmajew

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 ...

Elsevier Science Inc2016

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Parallel algorithms for tensor completion in the CP format

Daniel Kressner, André Uschmajew

Low-rank tensor completion addresses the task of filling in missing entries in multidimensional data. It has proven its versatility in numerous applications, including context aware recommender systems and multivariate function learning. To handle large-sc ...

Elsevier Science Bv2016

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

Fabio Nobile, Daniel Kressner, Francesca Bonizzoni

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 ...

Elsevier2016

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

Daniel Kressner, Meiyue Shao, Bo Kågström

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 ...

Assoc Computing Machinery2015

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

Fabio Nobile, Christine Tobler, Daniel Kressner, Rajesh Kumar

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 ...

2015

Low rank differential equations for Hamiltonian matrix nearness problems

Daniel Kressner

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axi ...

Springer2015

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

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 ...

Wiley-Blackwell2015

Bivariate Matrix Functions

Daniel Kressner

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 ...

Element2014

On the eigenvalue decay of solutions to operator Lyapunov equations

Daniel Kressner

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 ...

Elsevier Science Bv2014

Optimally Packed Chains of Bulges in Multishift QR Algorithms

Daniel Kressner

The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A. After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom right corner along ...

Association for Computing Machinery2014

Generalized eigenvalue problems with specified eigenvalues

Daniel Kressner

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 ...

Oxford University Press2014

On A Perturbation Bound For Invariant Subspaces Of Matrices

Daniel Kressner

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 ...

Siam Publications2014

Nonlinear Eigenvalue Problems With Specified Eigenvalues

Daniel Kressner

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed al ...

Siam Publications2014

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

Daniel Kressner, Michael Maximilian Steinlechner, André Uschmajew

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 ...

Siam Publications2014

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Daniel Kressner

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...

Wiley-Blackwell2014

An indefinite variant of LOBPCG for definite matrix pencils

Daniel Kressner, Meiyue Shao

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 ...

Springer2014

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