Title: “Computing many eigenpairs of a Hermitian matrix”
Dr. Eugene Vecharynski
Lawrence Berkeley National Laboratory
When: 3:10 – 4:00pm, Friday, May 8, 2015
Where: 3083 Kemper Hall
Host: Zhaojun Bai
The talk will address computation of large subsets of lowest eigenpairs of Hermitian matrices. This type of problem arises, for example, in the context of Kohn-Sham Density Functional Theory based electronic structure calculation for large molecular systems or solids. Because of the large number of targeted eigenpairs (on the order of thousands or more), standard solution techniques are not efficient due to the need of repeatedly solving a large dense eigenvalue problem, given by the Rayleigh–Ritz procedure, which is costly and poorly scalable. In this talk, I will introduce the Projected Preconditioned Conjugate Gradient (PPCG) algorithm that performs significantly fewer Rayleigh–Ritz calculations, and as a result is substantially faster than standard approaches. An experimental distributed memory version of the PPCG algorithm has been implemented within Quantum Espresso and QBox electronic structure packages.
3083 Kemper Hall