Block algorithms with augmented Rayleigh-Ritz projections for large-scale eigenpair computation
主 题: Block algorithms with augmented Rayleigh-Ritz projections for large-scale eigenpair computation
报告人: 刘浩洋，16级计算系硕士，导师文再文老师，研究方向是最优化和特征值计算 (北京大学)
时 间: 2016-10-14 12：00-13：15
地 点: 理科一号楼 1560
Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate eigenpairs. So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner. In this work, we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods. To achieve a competitive speed, we propose an augmented Rayleigh-Ritz (ARR) procedure. Combining this ARR procedure with a set of polynomial accelerators, as well as utilizing a few other techniques such as continuation and deflation, we construct a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps. Extensive computational experiments are conducted in Matlab on a representative set of test problems to evaluate the performance of two variants of our algorithm. Numerical results, obtained on a many-core computer without explicit code parallelization, show that when computing a relatively large number of eigenpairs, the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers. 报名方式：请有意参加的老师在10月13日（周四）晚10点前发送邮件至smsxueshu@126.com,我们将回复邮件和您确认,邮件报名方式仅限于老师，有意参加的同学请点击报名链接 http://www.sojump.hk/jq/9964858.aspx
