Folded spectrum method

In mathematics, the folded spectrum method (FSM) is an iterative method for solving large eigenvalue problems. Here you always find a vector with an eigenvalue close to a search-value ε . This means you can get a vector Ψ in the middle of the spectrum without solving the matrix.

Ψ i + 1 = Ψ i − α ( H − ε 1 ) 2 Ψ i , with 0 < α < 1 and 1 the Identity matrix.

In contrast to the Conjugate gradient method, here the gradient calculates by twice multipling matrix H : G ∼ H → G ∼ H 2 .