Talk: Master's Thesis

Yesterday I gave a talk on the preliminary results of my master's thesis on Projection Methods for Generalized Eigenvalue Problems. Below is the announcement for the talk; it mentions only complex (Hermitian) matrices but all results are immediately applicable to real matrices. The slides are here (PDF).

Projection Methods for Generalized Eigenvalue Problems

In this talk, we will discuss backward errors, dense solvers, and a new projection method for generalized eigenvalue problems (GEPs) with Hermitian positive semidefinite (HPSD) matrices.

We will present properties and origins of such GEPs. We will also address quickly computable and structure preserving backward error bounds for these kinds of GEPs. There is an abundance of literature on backward error measures possessing one of these features but only recently, the author came across a backward error providing both.

We will elaborate on dense solvers for GEPs with HPSD matrices. The standard solver for GEPs with Hermitian matrices is fast but requires positive definite mass matrices and is only conditionally backward stable; the QZ algorithm for general GEPs is backward stable but it is also magnitudes slower and does not preserve any problem properties. In the talk, we will present two new backward stable and structure preserving solvers, one using deflation, the other one using the generalized singular value decomposition (GSVD). In comparison to the QZ algorithm, both solvers are competitive with the standard solver in our tests.

Finally, we will touch on a new solver for large, sparse GEPs.

Talk: Working Remotely with Secure Shell, Grid Engine, and Screen

On Monday, February 23, 2015, I gave a talk in the tools seminar at my university about three tools that are useful when working remotely on another computer and that I use a lot:

Regarding secure shell, I explained how to use several of the programs that are part of OpenSSH. Grid Engine is a software suite for cluster management and you have to use it in order to submit jobs to the cluster of the mathematics department at my university. Screen is a window manager for terminals and offers--among other things--persistent shell sessions. Screen is not a program for remote computer access but I felt that that persistent shell sessions integrate nicely with remote computer work.