In addition to those suggestions, here are a few more relevant to the present discussion. For dense matrices and how to think about linear algebra algorithms, I highly recommend Trefethen and Bau "Numerical Linear Algebra". For sparse direct solvers, Tim Davis' book (http://www.ec-securehost.com/SIAM/FA02.html) is good, and you can transition from the "learning"-level implementation to Umfpack which is his production-quality solver (it's what is behind Matlab's backslash).
For iterative solvers, Saad is pretty standard. For multiphysics solvers, I don't think any book can match the Knoll and Keyes' 2004 review on Jacobian-free Newton-Krylov methods (it's very accessible).
The GSL has better implementations for many general-purpose algorithms in NR. SciPy is great if you work in Python. For scalable linear and nonlinear solvers, look at PETSc.
Comments
You are probably familiar with this page
http://www.fceia.unr.edu.ar/~fisicomp/apuntes/biblios/wnotnr...
and the suggested alternatives
http://www.fceia.unr.edu.ar/~fisicomp/apuntes/biblios/altnr....
In addition to those suggestions, here are a few more relevant to the present discussion. For dense matrices and how to think about linear algebra algorithms, I highly recommend Trefethen and Bau "Numerical Linear Algebra". For sparse direct solvers, Tim Davis' book (http://www.ec-securehost.com/SIAM/FA02.html) is good, and you can transition from the "learning"-level implementation to Umfpack which is his production-quality solver (it's what is behind Matlab's backslash). For iterative solvers, Saad is pretty standard. For multiphysics solvers, I don't think any book can match the Knoll and Keyes' 2004 review on Jacobian-free Newton-Krylov methods (it's very accessible).
The GSL has better implementations for many general-purpose algorithms in NR. SciPy is great if you work in Python. For scalable linear and nonlinear solvers, look at PETSc.