Graduate numerical analysis books

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I am a first year graduate student, and I am looking for a good numerical analysis book to self-study. Ideally, I am looking for a book that introduces the basics of floating point arithmetic, interpolation, solutions to non-linear equations, and numerical methods in ODE's and PDE's. More importantly, I would like a book that has good exercises as well. I will most likely be taking a course on numerical PDE next term so I am looking for a book that would help me brush up on numerical analysis.