That article is quite right regarding the take-home message to try to avoid inverting a matrix when other, more direct methods for solving the particular problem at hand exist.<p>On page 2 of <a href="http:&#x2F;&#x2F;www.ti3.tuhh.de&#x2F;paper&#x2F;rump&#x2F;Ru08a.pdf" rel="nofollow">http:&#x2F;&#x2F;www.ti3.tuhh.de&#x2F;paper&#x2F;rump&#x2F;Ru08a.pdf</a> there is an innocent-looking matrix for which the numerically computed inverse is off from the true inverse by <i>47 orders of magnitude</i>.<p>However, one of the reasons he&#x27;s given is not correct: Druinsky and Toledo have shown (<a href="http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1201.6035" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1201.6035</a>) that -- despite the very widespread belief to the contrary -- solving a linear system be calculating the inverse can be as accurate (though not nearly as efficient) as solving it directly.<p>They even speculate as to how this myth was able to sustain it for so long. Namely, there is a certain error bound for the solution as calculated by employing the inverse which is quite simple to deduce and which predicts a pretty large error. However, this bound is too conservative. There is a better bound, which ensures that the error is of the same kind as for the direct method. However, this bound is much harder to derive.