Advances in Numerical Analysis

Research Article

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

Algorithm 1

Input:
 Initial vector π‘₯ 0
begin
 Set πœ† 1 ( 1 ) = π‘₯ 𝑇 0 𝐴 π‘₯ 0 π‘₯ 𝑇 0 𝐡 π‘₯ 0
 For   𝑗 = 0 , 1 , 2 , …
 begin
  Solve linear system 𝐴 𝑧 𝑗 + 1 = 𝐡 π‘₯ 𝑗 for 𝑧 𝑗 + 1
  Set πœ† 1 ( 𝑗 + 1 ) = 𝑧 𝑇 𝑗 + 1 𝐴 𝑧 𝑗 + 1 𝑧 𝑇 𝑗 + 1 𝐡 𝑧 𝑗 + 1
  Set π‘₯ 𝑗 + 1 = 𝑧 𝑗 + 1 β€– 𝑧 𝑗 + 1 β€–
  Output:   π‘₯ 𝑗 , πœ† 1 ( 𝑗 )
 end
end