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I'm using a lot of linear solvers and preconditioners, but mostly, they are magical black boxes to me. Since I'll also have to implement some of them in future, I would like to learn a bit more, exactly how they work an which one is "good" for what.

Since I'm quite fit in the basics (linear algebra, numerics), I do not need a book that covers the full theory. I'm more looking for an extensive, well-understandable description of the various algorithms. Something like a "cook book".

Any recommendations?

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Have a look at Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Barrett et al.). You can find it here.

Here's why I'm recommending this over other references:

  1. the "flowchart of iterative methods" in appendix D (last page)
  2. covers both linear solvers and preconditioners,
  3. it is short (100 pages or so),
  4. does not go into too much detail,
  5. has a list of references if you're curious to find out more about a particular solver/preconditioner,
  6. the writing style is very clear and the authors are well-known experts in the field,
  7. it is free to download and print.

Caveat: this book was written in 1994 so it may not describe some of the more recent developments...

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