Big picture discussion for iterative linear solvers? The Numerical Recipes book provides a great discussion and insight regarding direct solvers for linear systems (chap 2). Is there an equivalent big picture discussion for iterative methods in the literature?
 A: You can consider the book
Barrett, Richard; Berry, Michael; Chan, Tony F.; Demmel, James; Donato, June; Dongarra, Jack; Eijkhout, Victor; Pozo, Roldan; Romine, Charles; van der Vorst, Henk, Templates for the solution of linear systems: building blocks for iterative methods, Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiii, 112 p. (1993). ZBL0814.65030.
It is dedicated only to the iterative solver, maybe in some way can be consider near Numerical Recipes.
Also maybe can be useful the chapter 4 of:
Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto, Numerical mathematics, Texts in Applied Mathematics. 37. New York, NY: Springer. xx, 654 p. (2000). ZBL0957.65001.
These suggestions are very subjective.

If we consider sparse linear system, a very big area where iterative solver are used, I think that the "standard" reference is
Saad, Yousef, Iterative methods for sparse linear systems., Philadelphia, PA: SIAM Society for Industrial and Applied Mathematics. xviii, 528 p. (2003). ZBL1031.65046.
You can find the pdf at this link

I suggest also this question of scicomp that it is interesting.
