(1) 𝑤 1 = 𝑒 𝑇 1 , 𝑧 1 = 𝑒 1 , 𝑑 1 = 𝑎 1 1 .
(2) for 𝑗 = 2 to 𝑛   do
(3)   𝑤 𝑗 = 𝑒 𝑇 𝑗 , 𝑧 𝑗 = 𝑒 𝑗 .
(4)  for   𝑖 = 1 to 𝑗 1 do
(5)    𝐿 𝑗 𝑖 = 𝐴 𝑗 , 𝑧 𝑖 𝑑 𝑖 , 𝑈 𝑖 𝑗 = 𝑤 𝑖 𝐴 , 𝑗 𝑑 𝑖
(6)   apply a dropping rule to 𝐿 𝑗 𝑖 and to 𝑈 𝑖 𝑗
(7)    𝑧 𝑗 = 𝑧 𝑗 𝑤 𝑖 𝐴 , 𝑗 𝑑 𝑖 𝑧 𝑖 ,   𝑤 𝑗 = 𝑤 𝑗 𝐴 𝑗 , 𝑧 𝑖 𝑑 𝑖 𝑤 𝑖
(8)   for all 𝑙 𝑖 apply a dropping rule to 𝑧 𝑙 𝑗 and to 𝑤 𝑗 𝑙
     (first format of dropping for 𝑊 and 𝑍 )
(9)   end for
(10) for all 𝑙 𝑗 apply a dropping rule to 𝑧 𝑙 𝑗 and to 𝑤 𝑗 𝑙
      (second format of dropping for 𝑊 and 𝑍 )
(11)   𝑑 𝑗 = 𝑤 𝑗 𝐴 , 𝑗 (if 𝐴 is not positive definite)
(12)   𝑑 𝑗 = 𝑤 𝑗 𝐴 𝑤 𝑇 𝑗 (if 𝐴 is positive definite)
(13) end for
(14) Return 𝐿 = ( 𝐿 𝑖 𝑗 ) and 𝑈 = ( 𝑑 𝑖 𝑈 𝑖 𝑗 )
Algorithm 1: ILUFF algorithm.