Given a linear algebra problem and an approximate solution, can we say something about the quality of the given approximate solution without knowing an exact solution?

Continue reading Evaluating Approximate Solutions using the Backward Error

Given a linear algebra problem and an approximate solution, can we say something about the quality of the given approximate solution without knowing an exact solution?

Continue reading Evaluating Approximate Solutions using the Backward Error

Currently, AHCI is the standard interface between a host and SATA storage devices. Windows XP does not come with a built-in AHCI driver which may prevent it from detecting a computer's storage device. I describe a common solution to this problem and how it worked out for me.

Last week I replaced Gentoo Linux with LXLE on my parents' computer. Gentoo is a very flexible distribution but it was overkill for my parents who use their computer only to browse the web and send e-mails. Moreover, the build times for Firefox and LibreOffice were really long so I wanted a replacement for Gentoo. Ideally, the new distribution should be lightweight, popular, have long-term support, and provide binaries. Lubuntu and LX**L**E caught my attention because they were using LX**D**E, a no-frills desktop environment. After testing these distributions in a QEMU/KVM virtual machine, I decided to install LXLE because of the preinstalled weather app Typhoon and the random wallpaper switch in the taskbar.

Higham's *Accuracy and Stability of Numerical Algorithms* is regularly needed for my work. The second edition of the book was released in 2002 so some of the bounds do not reflect the state of the art in 2015. I collected some papers with improved bounds which are relevant for me.

Continue reading Improved Error Bounds for "Accuracy and Stability of Numerical Algorithms"

In the mathematical literature, numerous bounds can be found for the spectral norm of a matrix. Can we improve these bounds if the matrices are known to be Hermitian or even real symmetric semidefinite?

Continue reading Spectral Norm Bounds for Hermitian Matrices

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.

You can download the presentation slides here (PDF).

On October 20, 2014 Cornelia Gamst and me gave a short talk on Git (Wikipedia) in the tools seminar at the Berlin Institute of Technology. The target audience were people who did not know what a version control system is or who had not used Git before hence we gave reasons why revision control is a good thing and why we use Git for it. The Git introduction itself was brief and included only the basic workflow though we had the opportunity to demonstrate some of the more powerful Git abilities during the hands-on exercise.

The slides are available from the website of the tools seminar.

This blog is running on WordPress and the current theme Twenty Fourteen allows the browser to hyphenate words. This looked bad so I disabled this feature by creating a child theme. A tutorial for creating a child theme can be found here and the required the new CSS file is here.

xPTEQR is a LAPACK function for the computation of the eigendecomposition of a symmetric positive definite tridiagonal matrix. I compare the performance and accuracy of xPTEQR to the other symmetric eigensolvers in LAPACK 3.5.0.

In layman’s terms, there are several algorithms available on a computer that calculate the eigenvectors and eigenvalues of matrices with special properties (symmetric, positive definite, tridiagonal). xPTEQR is the name of the computer implementation of one of those algorithms and I am not aware of any measurements with it. In this blog post I compare xPTEQR in terms of speed and accuracy to other good algorithms. In the figures below, xPTEQR can be found under the label "SVD" (xPTEQR is the name of the implementation, SVD is the algorithm). Moreover, in every figure it holds that lower is better.

Yesterday I bought an SSL certificate and changed my password so that I can securely log into this blog.

I want every reader of this blog to benefit from the available encryption and to that end the blog software forwards all HTTP connections to HTTPS from now on.