Daniel Kressner@_kreda_Aug 24GPT-5.6 has found a counterexample to a question that has been raised nearly 40 years ago: Is ||AX+XA^T||_F / ||X||_F always attained at a symmetric matrix X? arxiv.orgA counterexample to the symmetric-maximizer conjecture for...It has been conjectured that the operator norm of the Lyapunov operator induced by the Frobenius norm is always attained at a symmetric matrix. The conjecture is known to hold for all matrices of...92934330K
Daniel Kressner@_kreda_Aug 17Ever wondered how to solve a real skew-symmetric or orthogonal eigenvalue problem? There is now a new solver based on simple ingredients! arxiv.orgHalving the size of skew-symmetric eigenvalue problems via the...This paper introduces a novel algorithm for computing eigenvalues and eigenvectors of a dense real skew-symmetric matrix $A$. Its main ingredient is the computation of a polar factor of $A$ that...36473
Daniel Kressner@_kreda_Jun 16New preprint with Zvonimir Bujanović and Hrvoje Olić on Stochastic trace estimation with tensor train random vectors arxiv.orgStochastic trace estimation with tensor train random vectorsStochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured settings,...5315
Daniel Kressner@_kreda_Feb 6Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop arxiv.orgLinear Systems and Eigenvalue Problems: Open Questions from a...This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear...14845K
Daniel Kressner@_kreda_Oct 23, 2025Finally out: Speeding up Dynamical Low-Rank Approximation with Discrete Empirical Interpolation arxiv.orgInterpolatory Dynamical Low-Rank Approximation: Theoretical...Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time-dependent...2217
