I'd be tempted to add Numerical Recipes in C to the second list. I've often referred to it for various algorithmic problems thinking that it will be helpful and practical (examples in C!), but I'm usually disappointed. Most of it is targeted at very technical, math heavy problems. But hey, should my job require use of Toeplitz Matrices, NR is just an arm's length away!
This is NOT at all a knock on the book, since the title makes quite clear what it's about. But for whatever reason this one seems to end up on various "good to have on your shelf" lists when it probably isn't.
Eg. my professor owned NRC, and he did use it, especially the CD, to take algorithms as a plug-and-play starting point when doing some numerical analysis. Of course, you can also get similar algorithms off the web, but some professors are old-school like that.
This is NOT at all a knock on the book, since the title makes quite clear what it's about. But for whatever reason this one seems to end up on various "good to have on your shelf" lists when it probably isn't.