矩阵计算系列讲座
报告人：李仁仓 教授（美国特克萨斯大学阿灵顿分校）
Talk 1: Conditioning of Vandermone Matrix
2022年12月6日： 9:00-10:15
腾讯会议：152-837-946
摘要：In this talk, we will present various results on asymptotically optimal lower bounds on the condition numbers of real rectangular Vandermonde matrices.
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Talk 2: Vandermone Matrix and Convergence of Krylov Subspace Methods
2022年12月6日： 10:30-11:45
腾讯会议：152-837-946
摘要：Rectangular Vandermonde matrices play a crucial role in the convergence analysis of Krylov subspace methods for linear systems and eigenvalue problems. In this talk, we will present various results on the sharpness of the existing error bounds for CG, MINRES, and the Lanczos method for the symmetric eigenvalue problem.
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Talk 3: ADI Method for Sylvester Equations
2022年12月7日： 9:00-10:15
腾讯会议：548-255-673
摘要：We are concerned with numerical solutions of large scale Sylvester equations, Lyapunov equations as a special case in particular included, with the right-hand sides having very small rank. For stable Lyapunov equations, it has been demonstrated that the so called Cholesky factored Alternating-Directional-Implicit (ADI) method with decent shift parameters can be very effective. In this talk we'll present a generalization of Cholesky factored ADI for Sylvester equations. We also demonstrate that often much more accurate solutions than ADI solutions can be gotten by performing Galerkin projection via the column space and row space of the computed approximate solutions.
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Talk 4: Optimization on Stiefel Manifold and Nonlinear Eigenvalue Problem
2022年12月7日： 10:30-11:45
腾讯会议：548-255-673
摘要：Optimization problems on Stiefel Manifolds arise frequently in machine learning models. In this talk, we will present a solution framework via NEPv (nonlinear eigenvalue problem with eigenvector dependency) to solve such problems.
邀请人:张雷洪