  Computing the Wasserstein barycenter of a set of probability measures under
the optimal transport metric can quickly become prohibitive for traditional
second-order algorithms, such as interior-point methods, as the support size of
the measures increases. In this paper, we overcome the difficulty by developing
a new adapted interior-point method that fully exploits the problem's special
matrix structure to reduce the iteration complexity and speed up the Newton
procedure. Different from regularization approaches, our method achieves a
well-balanced tradeoff between accuracy and speed. A numerical comparison on
various distributions with existing algorithms exhibits the computational
advantages of our approach. Moreover, we demonstrate the practicality of our
algorithm on image benchmark problems including MNIST and Fashion-MNIST.
