Can anyone give me some nice references for the following topics at graduate level:

1) Iterative methods for linear systems: Jacobi Method, Gauss-Seidel Method, conjugate gradient method;

2) Linear and non-linear least squares;

3) Numerical integration: Newton Cotes, Romberg integration, gaussian quadrature, error analysis;

4) Numerical Methods for ordinary differential equations: Finite differences, Taylor, Runge-Kutta;

I'm looking for something very rigorous.


  • 1
    $\begingroup$ Check Numerical Analysis: A Mathematical Introduction 1st Edition by Michelle Schatzman. Absolutely wonderful book. $\endgroup$ – Artem Dec 23 '17 at 15:48
  • 2
    $\begingroup$ I like Rainer Kress's Numerical Analysis for that purpose. Everything is built on functional analysis, so it's about as rigorous as you need. $\endgroup$ – user14717 Dec 23 '17 at 22:24
  • $\begingroup$ I also like "Theoretical Numerical Analysis" by Kendall Atkinson, but I don't like it quite as much as Kress. $\endgroup$ – user14717 Dec 23 '17 at 22:26

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