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 \varepsilon. This means you can get a vector \Psi in the middle of the spectrum without solving the matrix.

\Psi_{i+1}= \Psi_i-\alpha( H- \varepsilon \mathbf{1} )^2 \Psi_i, with 0<\alpha^{\,}<1 and \mathbf{1} the Identity matrix.

In contrast to the Conjugate gradient method, here the gradient calculates by twice multiplying matrix H:\;G\sim H\rightarrow G\sim H^2.

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