主讲人：许进超 教授 美国宾州大学
摘要：In this talk, I will present a general framework for the design and analysis of Algebraic or Abstract Multi-Grid (AMG) methods. Given a smoother, such as Gauss-Seidel or Jacobi, we provide a general approach to the construction of a quasi-optimal coarse space and we prove that under appropriate assumptions the resulting two-level AMG method for the underlying linear system converges uniformly with respect to the size of the problem, the coefficient variation, and the anisotropy. Our theory applies to most existing multigrid methods, including the standard geometric multigrid method, the classic AMG, energy-minimization AMG, unsmoothed and smoothed aggregation AMG, and spectral AMGe. These results are summarized in a recent survey article entitled “Algebraic Multigrid Methods” in Acta Numerica (Vol 26). Finally we will discuss our ongoing investigation on relationship and cross-application between algebraic multigrid techniques and deep neural networks.