Publications de Daniel Kressner

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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 ...

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 ...

It is well known that a family of n×n commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider th ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

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 ...

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

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 ...

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 ...

We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A. ...

The problem of finding a k x 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 can a ...

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

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 with small bandwidth, w ...

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas-Anderson (AAA) method is one approach to construct such approximants numerically. F ...

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 ...

Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importan ...

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. ...

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 ...

The pseudospectral abscissa and the stability radius are well-established tools for quantifying the stability of a matrix under unstructured perturbations. Based on first-order eigenvalue expansions, Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2 ...

Daniel Kressner

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

A block algorithm for computing antitriangular factorizations of symmetric matrices

Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

Continuation Methods For Riemannian Optimization

Nonlinear Eigenvalue Problems With Specified Eigenvalues

Low rank differential equations for Hamiltonian matrix nearness problems

A simple, randomized algorithm for diagonalizing normal matrices

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

A fast spectral divide-and-conquer method for banded matrices

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Fast global spectral methods for three-dimensional partial differential equations

RANDOMIZED SKETCHING OF NONLINEAR EIGENVALUE PROBLEMS

Parallel algorithms for tensor completion in the CP format

A Parallel QZ Algorithm For Distributed Memory HPC Systems

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

Fast Computation Of Spectral Projectors Of Banded Matrices

Subspace Methods For Computing The Pseudospectral Abscissa And The Stability Radius