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

Algorithm 1

IKJ variant of ILU factorization with a static pattern 𝒮.

Input: Matrix 𝐴, the nonzero pattern 𝒮

Output: Matrix 𝐴 containing 𝐿 and 𝑈

for  each(𝑖,𝑗)∉𝒮  do

  𝑎_𝑖𝑗=0

end

for  𝑖=2,...,𝑛  do

  for  𝑘=1,…,𝑖−1 and (𝑖,𝑘)∈𝒮  do

  𝑎_𝑖𝑘←𝑎_𝑖𝑘/𝑎_𝑘𝑘

  for  𝑗=𝑘+1,...,𝑛and(𝑖,𝑗)∈𝒮  do

   𝑎_𝑖𝑗←𝑎_𝑖𝑗−𝑎_𝑖𝑘𝑎_𝑘𝑗

  end

 end

end