There isn't a single authoritative reference. It really depends on what you're doing. Numerical analysis and scientific computing are huge fields. If you have a

There isn't a single authoritative reference. It really depends on what you're doing. Numerical analysis and scientific computing are huge fields. If you have a specific area you're interested in, I can probably point you in the right direction. (Source: I did a PhD and postdoc in this field and research and develop numerical methods every day in industry. I have... a lot of books on this topic.)