Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century: History, Current Developments, and Future Perspectives

Algorithm 2

ILUT(𝜌,𝜏) computation.

Input: Matrix 𝐴, the user-specified parameters 𝜌 and 𝜏

Output: Matrices 𝐿 and 𝑈

for  𝑖=1,…,𝑛  do

 𝐰=𝐚_𝑖

 for  𝑘=1,…,𝑖−1 and 𝑤_𝑘≠0  do

  𝑤_𝑘←𝑤_𝑘/𝑎_𝑘𝑘

  if  𝑤_𝑘≥𝜏‖𝐚_𝑖‖₂  then

    𝐰←𝐰−𝑤_𝑘𝐮_𝑘

  else

   𝑤_𝑘=0

  end

 end

 Retain the 𝜌 largest entries in  w

 for  𝑗=1,…,𝑖−1  do

   𝑙_𝑖𝑗=𝑤_𝑗

 end

 for  𝑗=𝑖,…,𝑛  do

    𝑢_𝑖𝑗=𝑤_𝑗

 end

end