Reference on constructing preconditions (beginner level) I took linear algebra course this semester (as you've probably noticed looking at my previously asked questions!). We had a session on preconditioning, what are they good for and how to construct them for matrices with special properties. It was a really short introduction for such an important research topic, so I'm not sure if I got familiar with them. I need some elementary sources on it to be able to construct preconditions for famous matrices and to make sure I fully understand the concept. Any helps would be greatly appreciated. 
 A: It is still a very hot topic of Numerical Linear Algebra - The main question is to improve the conditioning of a (usually very large and potentially ill-conditioned) matrix.
Take a look at the work of Dongarra: Preconditioning Techniques
A good textbook is:
H. A. van der Vorst, Iterative Krylov Methods for Large Linear systems, 
Cambridge University Press, Cambridge, 2003.
A: Look what I have here in my bookshelves: the original thesis by Henk (H.A.) van der Vorst where it all started with , titled : Preconditioning by Incomplete Decompositions (1982). If you can lay your hands on it ..
A: *

*Here's a famous survey paper that may be too long: Preconditioning
Techniques for Large Linear Systems: A Survey by Michele
Benzi

*Then there's this shorter introduction that is heavy on computer
programming and matlab:
http://www.asc.tuwien.ac.at/~winfried/teaching/106.079/SS2011/downloads/script-p-106-122.pdf
It has an intimidating wall of formulas on an early page but gets
good again later.

*Also, this link seemed mildly interesting:
wwwhome.math.utwente.nl/~botchevma/nla/


Lecture 2 has a page with simple formulas for preconditioners, and assignment 2 had a lot of work on preconditioners.
I'm not sure which famous matrices you would like to see (special lknear group, upper triangular, permutation matrix, sparse, etc.) but I hope this helps.
