Inverting a sparse Matrix

Question

I have a sparse, square, symmetric matrix with the following structure: (Let's say the size of the matrix is N x N)

Here, the area under the blue stripes is the non-zero elements. Could someone tell me if there is a algorithm to invert this kind of matrix that is simple yet more efficient than Gaussian elimination and LU decomposition? Thank you in advance.

Your question is off-topic here, it is less about programming, more about Maths or Numerics. — usr1234567, Dec 02 '15 at 20:34
Could you tell me a more appropriate forum to address this kind of question? Thanks. — rnels12, Dec 02 '15 at 20:40

score 0 · Answer 1 · answered Dec 02 '15 at 20:29

0

Cholesky factorization is faster, O(n²). Or some specialized multi-band solvers, if you know the number of non-zero off-diagonals.

You can also apply iterative methods, maybe with preconditioning, it depends on your purpose.

answered Dec 02 '15 at 20:29

usr1234567

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score -1 · Answer 2 · answered Dec 02 '15 at 20:33

-1

There are a lot of sparse solvers. This can easily be solved using libeigen. What solver you choose is really going to depend on the properties of the sparse matrix besides the structure. Hope this helps.

answered Dec 02 '15 at 20:33

mculp

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Does not answer the question. He still has to choose an algorithm from Eigen. – usr1234567 Dec 02 '15 at 20:34

Inverting a sparse Matrix

2 Answers2