[Nikhil Bajaj]

Originally Posted by Michael Hill

The reason I say it's computationally intensive is this article: http://www.johndcook.com/blog/2010/0...t-that-matrix/

That article is 100% correct. The solutions above that are solving in a handful of seconds or less are not inverting the matrix. Reducing the matrix to reduced-row echelon form is related to what methods like LU and Cholesky factorization do.

Even normal Gaussian elimination will be pretty fast on a sparse matrix (though still slower than most methods above), but it has problems with numerical stability that get worse and worse as matrix size increases and is for that main reason avoided by most people solving numerical linear algebra problems.