5 papers
A counterexample to the symmetric-maximizer conjecture for Lyapunov operators
Daniel Kressner, Bart Vandereycken
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…
Halving the size of skew-symmetric eigenvalue problems via the polar decomposition
Daniel Kressner, Simon Mataigne
This paper introduces a novel algorithm for computing eigenvalues and eigenvectors of a dense real skew-symmetric matrix . Its main ingredient is the computation of a polar fact…
A mixed precision algorithm for the matrix square root
Bowen Gao, Daniel Kressner, Meiyue Shao
Mixed precision algorithms can significantly enhance the performance of linear algebra solvers by leveraging increasingly powerful low precision hardware while recovering working p…
Linear convergence of iterative contour integral-based eigensolvers for nonlinear eigenvalue problems
Daniel Kressner, Yuqi Liu, Jose E. Roman +2
Solving nonlinear eigenvalue problems is an important and challenging task in scientific computing. Contour integral-based approaches are attractive for such eigenvalue problems be…
Lanczos with compression for symmetric eigenvalue problems
Angelo A. Casulli, Daniel Kressner, Nian Shao
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix . Usually based on polynomial fi…