I need to find the vector x in the problem A.x = b

I have matrix A and vector b.

Inverting the matrix would do it, but in my case, the matrix is quite big. Luckily, it is extremelly sparse (lots of 0), so I guess there could be some way to take advantage of it.

The best approach I found is the Biconjugate Gradient method. Doing LU decomposition is too slow.

The exact answer is not needed. I only need to get x to a reasonable accurate result, so I think there could exist some methods using random numbers, annealing or something else faster than Biconjugate Gradient.

Someone has some ideas?

Best regards