Reference that Explains Preconditioning

Question

I would like to understand Preconditioning techniques and why they work. Could someone provide a good reference for this type of information?

Answer 1

Yousef Saad's book "Iterative methods for linear systems" is a good place to start. You can download the 1st edition for free from Saad's website,

http://www-users.cs.umn.edu/~saad/books.html

A good background in linear algebra and mathematical analysis is required.

The construction of good preconditioners is more of an art than an actual science and typically a good deal of knowledge about the actual application is required.

More recent work in preconditioners include the use of banded preconditioners. I would recommend the work done by the people of the PSKIKE project at http://www.pspike-project.org/