Sparse matrix inversion

Zhivago

Hello everyone!

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

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fresh_42

Mentor
2018 Award
If it has a lot of zeroes, the simple school method could do: solve a subsystem and substitute the solution into the rest. Also block multiplication could be appropriate, depending on the matrix. Another idea is to split it into a symmetric and a skew symmetric part.

"Sparse matrix inversion"

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