No.  They're both O(N^3) in the dimension of the matrix.  And it's more stable only in the sense that it's doing fewer operations.  There's actually a great trick (again, in Numerical Recipes) when doing inversion to spend a few more (constant factor) cycles to iterate a correction to the limit of the precision of your number representation.<p>Really, check Numerical Recipes.  I like their section a lot, though I don't have my copy handy to give you a cite.