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Are there any algorithms useful for inverting (non-symmetric) M-matrices?

https://en.wikipedia.org/wiki/M-matrix

I presumed that the extra condition of being an M-matrix could prove useful in algorithms for inverse calculations (notably the "stability" conditions mentioned on Wikipedia). With some Google searches I am not finding much.

We have the existence of the inverse and additionally $A^{-1} \geq 0$ ... can this generally help in calculation?

Jacob A
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    I've not heard of such an advantage, but it is a reasonable thing to be curious about. – hardmath Feb 02 '22 at 23:37
  • @JacobA One potential approach is to use the infinite series formula that I give in my post here. I don't know if that necessarily saves a lot of effort, though – Ben Grossmann Feb 03 '22 at 01:55
  • @Ben Grossmann Interesting, I actually saw your answer there earlier but didn't think of the application in this way... not sure how efficient that would be (and are there some error bounds?) If it helps at all for my case, your $B$ in that answer is stochastic (col sums are 1). Thanks! – Jacob A Feb 03 '22 at 03:39
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    In general, if the sum converges then we have $\left|(I - B)^{-1} - \sum_{k=0}^n B^n\right| \leq \frac{|B|^{n+1}}{1 - |B|}$ (for any matrix norm $|\cdot|$, e.g. the maximal absolute row sum). – Ben Grossmann Feb 03 '22 at 03:51
  • In my case it wouldn't be all that useful, as the original problem boils down to calculating a large power of a matrix anyway, which might at times be faster; but thank you! – Jacob A Feb 04 '22 at 17:42

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