@Article{Oshima2015, author = "Oshima, Toshio", title = "Katz's middle convolution and Yokoyama's extending operation", journal = "Opuscula Math.", year = "2015", volume = "35", number = "5", pages = "665--688", doi = "http://dx.doi.org/10.7494/OpMath.2015.35.5.665", url = "http://dx.doi.org/10.7494/OpMath.2015.35.5.665", abstract = "We give a concrete relation between Katz's middle convolution and Yokoyama's extension and show the equivalence of both algorithms using these operations for the reduction of Fuchsian systems on the Riemann sphere.", keywords = "Fuchsian systems, middle convolution", issn = "1232-9274" }