# if I want only one element of the inverse matrix, does there exist a fast algorithm?

I use Mathematica to solve problems. I have a question about matrix inverse.

if I want only one element of the inverse matrix, does there exist a faster algorithm than using Inverse to calculate the whole inverse matrix and extract the element which I want?

• This paper's abstract says they can calculate they diagonal of the inverse matrix in $\mathcal{O}(n^{\frac{3}{2}})$, but I don't know whether there's something for an arbitrary entry. – G. Bach Oct 17 '13 at 11:37
• The underlying issue here may be about Mathematics more than Computer Science. – Dukeling Oct 17 '13 at 11:38
• Here is something on more than just the diagonal for sparse matrices, and here is something on a parallel algorithm for structured sparse matrices. – G. Bach Oct 17 '13 at 11:42
• @G.Bach thank you for your information – user15964 Oct 17 '13 at 12:42
• @G.Bach Many of my answers are like that. Using google effectively is non-trivial. If the information is useful, then it answers the question. – Yuval Filmus Oct 18 '13 at 2:29