Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Algorithm 1

Recursive  procedure H_Inverse(𝑚,𝑥)

If the matrix m is partition then

 H_Inverse(𝑚₁₁,𝑥₁₁)

 𝑥₁₂=−𝑥₁₁⊙𝑚₁₂

 𝑥₂₁=−𝑚₁₂⊙𝑥₁₁

 𝑚₂₂=𝑚₂₂⊕𝑚₂₁⊙𝑥₁₂

 H_Inverse(𝑚₂₂,𝑥₂₂)

 𝑚₁₂=𝑥₁₂⊙𝑚₂₂

 𝑚₁₁=𝑚₁₁⊕𝑚₁₂⊙𝑥₂₁

 𝑚₂₁=𝑚₂₂⊙𝑥₂₁

else

 Direct_Inverse(𝑚₁₁)

end if