Good morning to everybody, we hope you had a great weekend and thanks to all for heroic efforts with project 1.

There are many really excellent reports. We look forward to send you feedback.

Last week we finalized our discussions of linear algebra methods, and in particular their relevance for project 1. 

We then started discussing project 2, which looks similar to project 1 but is now an eigenvalue problem A^u^=¦Ëu^. 

This week we will discuss in more detail project 2 and two popular algorithms for finding eigenvalues and/or transforming our matrix to a tridiagonal form and then finding the eigenvalues.  These algorithms are

1) The Jacobi method, which we will implement in project 2

2) Householder's algorithm for reducing a dense matrix to tridiagonal form and then Givens algorithm for finding the eigenvalues. Householder's algorithm is reckoned (still) as one of the top ten algorithms in Numerical mathematics. For a ranking, see

https://nickhigham.wordpress.com/2016/03/29/the-top-10-algorithms-in-applied-mathematics/

The Houselholder algo is part of the matrix factorization algorithms.

The material is covered by chapter 7 of the lecture notes and the eigenvalue slides, see for example http://compphysics.github.io/ComputationalPhysics/doc/pub/eigvalues/html/eigvalues-bs.html

Next week we will finalize the eigenvalue discussion part with a discussion of so-called iterative (Krylov) algorithms and the power method (which formed the basis for the google search algorithm). 

Lab this week: we work on project 2, no special lectures.  Only project work.

Best wishes to you all,

Morten et al