Long term: Integrate with other solvers

[mikolalysenko]

It would be great to eventually have this module work about as well as MATLAB's backslash operator.

In MATLAB though, the system selects the best linear solver from a large base of different possibilities depending on the structure of the input. As I understand it, the following methods are generally used:

• For dense square matrices, an LUP decomposition is computed
• For square dense positive semidefinite matrices, a Cholesky factorization is used
• For under/overdetermined systems MATLAB computes a linear least squares solution
• For sparse systems it uses iterative methods (like conjugate gradient)

Each of these algorithms should be implemented as a separate module, and the code here should select the best option given the input data.

[mikolalysenko]

For reference, here is how MATLAB does it:

http://www.mathworks.com/help/matlab/ref/mldivide.html

If you click on "More about > Algorithms" you can see the flow chart that MATLAB uses to select the best solver for a given problem.