Advances in Numerical Analysis

Research Article

Partitioning Inverse Monte Carlo Iterative Algorithm for Finding the Three Smallest Eigenpairs of Generalized Eigenvalue Problem

Algorithm 2

input:
  𝐴 ∈ 𝑅 𝑛 Γ— 𝑛 , 𝑓 0 ∈ 𝑅 𝑛
begin
 Starting from initial vector 𝑓 0
 For   𝑗 = 1 , 2 , …
 begin
  Using global algorithm, calculate the sequence of Monte Carlo
  iterations by solving the following system
           𝐴 𝑓 𝑗 = 𝐡 𝑓 𝑗 βˆ’ 1
  Set
        πœ† ( 𝑗 ) = ⟨ 𝐴 𝑓 𝑗 , β„Ž 𝑗 ⟩ ⟨ 𝐡 𝑓 𝑗 , β„Ž 𝑗 ⟩ = ⟨ 𝐡 𝑓 𝑗 βˆ’ 1 , β„Ž 𝑗 ⟩ ⟨ 𝐡 𝑓 𝑗 , β„Ž 𝑗 ⟩
  Output:
  Smallest eigenvector πœ† 1 ( 𝑗 ) , and corresponding eigenvector 𝑓 𝑗 .
 end
end