(1) 𝑤 𝑛 = 𝑒 𝑇 𝑛 , 𝑧 𝑛 = 𝑒 𝑛 , 𝑑 𝑛 = 𝑎 𝑛 𝑛 .
(2) for   𝑗 = 𝑛 − 1 to 1 do
(3)   𝑤 𝑗 = 𝑒 𝑇 𝑗 , 𝑧 𝑗 = 𝑒 𝑗 .
(4)  for 𝑖 = 𝑗 + 1 to 𝑛   do
(5)    𝑈 𝑗 𝑖 = 𝐴 𝑗 , ∶ 𝑧 𝑖 𝑑 𝑖 , 𝐿 𝑖 𝑗 = 𝑤 𝑖 𝐴 ∶ , 𝑗 𝑑 𝑖
(6)   apply a dropping rule to 𝑈 𝑗 𝑖 and to 𝐿 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 = ( 𝑑 𝑗 𝐿 𝑖 𝑗 ) and 𝑈 = ( 𝑈 𝑖 𝑗 )
Algorithm 2: IULBF algorithm.