What are some recommended textbooks for implementing numerical algorithms?

[Somefantastik]

Maybe I missed the numerical methods books in the textbook forum? But I'd like a few suggestions on good texts that are descriptive in implementing numerical algorithms like root-finding, numerical integration, numerical interpolation, etc. I was about to buy Numerical Recipes

But I noticed in the comments that the algorithms are copyrighted.. so it's straight-up illegal to use that book in practice. There's hundreds of numerical methods books on amazon, can someone suggest one that they found useful? I have my undergrad book, which is TOO undergrad. I also have many books on FEM and numerical linear algebra, so I'm looking for one that covers a more general swath of topics. It must give detailed theory of stability, convergence, etc.

 

[marcusl]

I have the first edition of Stoer and Bulirsch. It's not the easiest book to read because it assumes some mathematical sophistication, but it does motivate the math results before discussing solution approaches and their properties and behaviors.