Weekly update for week 38

Welcome back to a new exciting week!!

Last week we discussed methods for solving eigenvalue problems, with an emphasis on the Jacobi method and project 2.

This week we will continue with a discussion of project 2 and look at so-called QR transformations, with an emphasis on Householder's method and algorithms for finding eigenvalues of tridiagonal matrices. We will also discuss iterative Krylov methods (Lanczos's algorithm in particular and if we get time also power methods.

The material is discussed in chapter 7 of the lecture notes and the slides on eigenvalues. 

Else, if we get time, we will start a discussion of ordinary differential equations (chapter 8 of the lecture notes).  These equations are everywhere in science and will prepare us for the solution of project 3. 

At the lab we will sneak a small session on how to understand vectorization and thereby increase the performance of our programs by simple compiler flags. See the material on vectorization at for example http://compphysics.github.io/ComputationalPhysics/doc/pub/codeoptimization/html/codeoptimization-bs.html

We will also show some simple demonstrations of makefiles (and hopefully cmake as well).

Best wishes to you all,

Anders, Anna, Mathis, Morten and Sebastian