Implementions of "Interior Point Method" to solve LP (and QP)

Another open source interior point linear programming solver is GLPK written in C: http://www.gnu.org/software/glpk/ and http://en.wikibooks.org/wiki/GLPK

The linear programming book by Bob Vanderbei (http://www.princeton.edu/~rvdb/LPbook/) is a good book for explaining the use of interior point algorithms for quadratic programming. The cited website also has links to software, but it doesn't seem to be "commercial quality" software. Vanderbei also has LOQO, a more industrial strength interior point code for quadratic programming (http://www.princeton.edu/~rvdb/ps/loqo5.pdf). Another recent idea in interior point qp is: http://www-personal.umich.edu/~murty/Grav-QP.pdf

Simplex methods and interior point methods both have their place. One is not better or faster than the other in general and you will find that each method performs better on different classes of problems.

As for codes, the open source Coin-OR project, Clp has Simplex, Dual Simplex, and Interior Point methods implemented in C++.

However, if you are just looking to solve a system of linear or quadratic equations of the form f(x) = 0, then this is not what you want at all. If the system you want is linear, then you need to understand direct or iterative linear solvers. If the problem is nonlinear, you should look into Newton's method or quasi-Newton methods.

best of luck.