28 citations · 72 across the 9 of their papers we have counts for
9 papers
Toward genuine efficiency and cluster robustness of preconditioned CG-like eigensolvers
Ming Zhou, Klaus Neymeyr
The performance of eigenvalue problem solvers (eigensolvers) depends on various factors such as preconditioning and eigenvalue distribution. Developing stable and rapidly convergin…
Angle-free cluster robust Ritz value bounds for restarted block eigensolvers
Ming Zhou, Andrew V. Knyazev, Klaus Neymeyr
Convergence rates of block iterations for solving eigenvalue problems typically measure errors of Ritz values approximating eigenvalues. The errors of the Ritz values are commonly…
Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation
Ming Zhou, Zhaojun Bai, Yunfeng Cai +1
Gradient-type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent it…
Convergence rates of individual Ritz values in block preconditioned gradient-type eigensolvers
Ming Zhou, Klaus Neymeyr
Many popular eigensolvers for large and sparse Hermitian matrices or matrix pairs can be interpreted as accelerated block preconditioned gradient (BPG) iterations in order to analy…
Majorization-type cluster robust bounds for block filters and eigensolvers
M. Zhou, M. E. Argentati, A. V. Knyazev +1
Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and the closely related research on properties of matrix-based signal filters are challenging, and…
Exponential convergence rates for Batch Normalization: The power of length-direction decoupling in non-convex optimization
Jonas Kohler, Hadi Daneshmand, Aurelien Lucchi +3
Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons beh…
Convergence theory for preconditioned eigenvalue solvers in a nutshell
Merico E. Argentati, Andrew V. Knyazev, Klaus Neymeyr +2
Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material…
A geometric convergence theory for the preconditioned steepest descent iteration
Klaus Neymeyr
Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, name…
Gradient flow approach to geometric convergence analysis of preconditioned eigensolvers
Andrew V. Knyazev, Klaus Neymeyr
Preconditioned eigenvalue solvers (eigensolvers) are gaining popularity, but their convergence theory remains sparse and complex. We consider the simplest preconditioned eigensolve…