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I'm in a numerical analysis course right now and it's pretty rigorous but I'm enjoying it a lot. I took a lower level course before that was more oriented towards implementation of numerical methods, so it's not my first time with the material.

Anyway, my professor wrote his own course notes and they're fantastic but I wanted some reference material since I'm currently outlining my own notes. Just wondering what the big ones out there are

edit: I would say I'm at an advanced undergraduate level

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  • $\begingroup$ Please consider adding the book-recommendation tag $\endgroup$
    – evaristegd
    Dec 22 '18 at 14:45
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Not sure what level you are looking for, but you might have a look at:

  • Numerical Methods for Scientists and Engineers, R. W. Hamming
  • Analysis of Numerical Methods, Isaacson and Keller
  • Numerical Mathematics and Computing by E. Ward Cheney and David R. Kincaid
  • Numerical Analysis, Burden and Faires
  • Theoretical Numerical Analysis: A Functional Analysis Framework, K. Atkinson, W. Han

The first two are Dover books, so the price is great, the last two are lots of dough. I do not have the last one, but it looks worthwhile checking out. The others I refer to often.

I think you can peruse them all online.

You might also want to check these out these other MSE postings:

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  • $\begingroup$ Nice recommendations, Amzoti (+1) $\endgroup$
    – amWhy
    Oct 3 '13 at 1:28
  • $\begingroup$ My goodness! Damn bee! But I'm glad they figured it out...hope you heal well and SOON! $\endgroup$
    – amWhy
    Oct 3 '13 at 1:33
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    $\begingroup$ Burden and Faires has lots of editions, so you can get some of the not-too-obsolete ones pretty cheap. $\endgroup$
    – Nate C-K
    Apr 4 '16 at 22:14
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You may also find this one interesting:

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Second Edition. Translated by R. Bartels, W. Gautschi, and C. Witzgall.

See here: https://www.springer.com/gp/book/9780387954523

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    $\begingroup$ broken link, please update $\endgroup$
    – Erik Hambardzumyan
    Sep 15 '18 at 11:51
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I like Numerical Recipes. Obsolete versions are free online.

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    $\begingroup$ Seconded. I like Numerical Recipes, too. The experts often sneer at the book because the algorithms are fairly simple, and occasionally don't work as well as the best-in-class ones. But the best-in-class ones are often so complicated that they are incomprehensible. Personally, I prefer something I can understand, even if it's a bit less than optimal. $\endgroup$
    – bubba
    Oct 3 '13 at 3:08
  • $\begingroup$ @bubba Ultimately I think if one wants something more complicated and specialized, it is better to search for it directly rather than in a general numerical analysis text. $\endgroup$
    – Simply Beautiful Art
    Oct 2 '20 at 12:46
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These are not really textbooks but free course materials available online from MITOpenCourseWare:

Introduction to Numerical Analysis - 2012

Introduction to Numerical Analysis - 2004

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I feel worth recommending the book [1] of Solomon Mikhlin. The first thing to say is that it is by no means an introductory level text: however, it offers a very accurate analysis of the error causes in numerical processes, along with the description of the "methods" which should be adopted to minimize/mitigate their effect. Definitely a worth second reading in numerical analysis.

[1] Mikhlin, Solomon G. Error analysis in numerical processes, Translated and revised from the German. Translated by Reinhard Lehmann, (English) Pure and Applied Mathematics, 1237. A Wiley-Interscience Series of Texts, Monographs and Tracts. Chichester: John Wiley & Sons Ltd., pp. 283 (1991), ISBN 0-471-92133-5, MR1129889, Zbl 0786.65038.

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