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.