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

Algorithm 5

Computation of the FSAI preconditioner.

Input: Matrix 𝐴 and the nonzero pattern 𝒮_𝐿

Output: Matrix 𝐺

for  𝑖=1,…,𝑛  do

 Compute 𝒥={𝑗∶(𝑖,𝑗)∈𝒮_𝐿}

 Set 𝑚=|𝒥|

 Gather 𝐴[𝒥,𝒥] from 𝐴

 Solve 𝐴[𝒥,𝒥]𝐠_𝑖[𝒥]=𝐢_𝑚

 𝐠_𝑖←𝐠_𝑖/√𝐠_𝑖,𝑚

end