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 $$\varepsilon$$. 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 $$H:\;G\sim H\rightarrow G\sim H^2.$$

Literature

 * https://web.archive.org/web/20070806144253/http://www.sst.nrel.gov/topics/nano/escan.html
 * https://web.archive.org/web/20070806144253/http://www.sst.nrel.gov/topics/nano/escan.html
 * https://web.archive.org/web/20070806144253/http://www.sst.nrel.gov/topics/nano/escan.html
 * https://web.archive.org/web/20070806144253/http://www.sst.nrel.gov/topics/nano/escan.html