Numerical Recipes has both sound theory exposition and working code (yes, with some bugs here and there). This blog post has neither. Nor, to my knowledge, does any other single reference out there. It's easily the best "how to think about numerics work" text I know; if you have a better one please point me there.
It's easy for a wonk to flame about something as pedestrian as a how-to text for working scientists, but it's really not helpful.
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
Numerical Recipes has both sound theory exposition and working code (yes, with some bugs here and there). This blog post has neither. Nor, to my knowledge, does any other single reference out there. It's easily the best "how to think about numerics work" text I know; if you have a better one please point me there.
It's easy for a wonk to flame about something as pedestrian as a how-to text for working scientists, but it's really not helpful.
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.