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Another great "intermediate" textbook (in my opinion) is Trefethen's Numerical Linear Algebra [1]. Much more readable than Golub's I would say, which is more like a reference than a textbook.

[1]: https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefet...

Strongly agree. This was actually the text book when I took numerical methods at MIT. As far as math texts go, it is definitely a joy to read.

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