• Numerical linear algebra
• Eigenvalue problems
• Adaptive finite elements

• M. Zhou, A.V. Knyazev, K. Neymeyr,
  Angle-free cluster-robust Ritz value bounds for restarted block eigensolvers.
  Numer. Linear Algebra Appl. online (2024), e2607. https://doi.org/10.1002/nla.2607.
• M. Zhou, K. Neymeyr,
  Convergence rates of individual Ritz values in block preconditioned gradient-type eigensolvers.
  Electron. Trans. Numer. Anal. 58 (2023), 597-620. https://doi.org/10.1553/etna_vol58s597.
• M. Zhou, M.E. Argentati, A.V. Knyazev, K. Neymeyr,
  Sharp majorization-type cluster robust bounds for block filters and eigensolvers.
  SIAM J. Matrix Anal. Appl. 44 (2023), 1852-1878. https://doi.org/10.1137/23M1551729.
• M. Zhou, Z. Bai, Y. Cai, K. Neymeyr,
  Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation.
  Numer. Linear Algebra Appl. 30 (2023), e2498. https://doi.org/10.1002/nla.2498.
• M. Zhou, K. Neymeyr,
  Cluster robust estimates for block gradient-type eigensolvers.
  Math. Comp. 88 (2019), 2737-2765. https://doi.org/10.1090/mcom/3446.
• J. Kohler, H. Daneshmand, A. Lucchi, T. Hofmann, M. Zhou, K. Neymeyr,
  Exponential convergence rates for Batch Normalization: The power of length-direction decoupling in non-convex optimization.
  Proceedings of Machine Learning Research 89 (2019), 806-815.
• M. Zhou,
  Convergence estimates of nonrestarted and restarted block-Lanczos methods.
  Numer. Linear Algebra Appl. 25 (2018), e2182. https://doi.org/10.1002/nla.2182.
• M. Zhou, K. Neymeyr,
  Sharp Ritz value estimates for restarted Krylov subspace iterations.
  Electron. Trans. Numer. Anal. 46 (2017), 424-446.
• M.E. Argentati, A.V. Knyazev, K. Neymeyr, E.E. Ovtchinnikov, M. Zhou,
  Convergence theory for preconditioned eigenvalue solvers in a nutshell.
  Foundations of Computational Mathematics 17 (2017), 713-727.
  Paper in arXiv library.   DOI: 10.1007/s10208-015-9297-1.
• K. Neymeyr, M. Zhou,
  Convergence analysis of restarted Krylov subspace eigensolvers.
  SIAM J. Matrix Anal. Appl. 37 (2016), 955-975.
  DOI:10.1137/16M1056481.
• M. Zhou, K. Neymeyr,
  Users' guide to the AMP Eigensolver (Adaptive Multigrid Preconditioned Eigensolver).
  Version 1.0, 2014.
• K. Neymeyr, M. Zhou,
  The block preconditioned steepest descent iteration for elliptic operator eigenvalue problems.
  Electron. Trans. Numer. Anal. 41 (2014), 93-108.
• K. Neymeyr, M. Zhou,
  Iterative minimization of the Rayleigh quotient by block steepest descent iterations.
  Numer. Linear Algebra Appl. 21 (2014), 604-617.
• K. Neymeyr, E. Ovtchinnikov, M. Zhou,
  Convergence analysis of gradient iterations for the symmetric eigenvalue problem.
  SIAM J. Matrix Anal. Appl. 32 (2011), 443-456.
• M. Zhou,
  On the convergence theory of preconditioned subspace iterations for eigenvalue problems.
  (Proceeding GAMM 2010) Proc. Appl. Math. Mech. 10 (2010), 553-554

Adaptive Multigrid Preconditioned Eigensolver: A software for the computation of the smallest eigenvalues and the associated eigenfunctions of a self-adjoint and elliptic partial differential operator in 2D domains.