Folded spectrum method

In mathematics, the folded spectrum method (FSM) is a 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

In contrast to the Conjugate gradient method, here the gradient calculates by twice multipling matrix $H:;Gsim\; H\; ightarrow\; Gsim\; H^2$

Literature

* J. K. L. MacDonald, Phys. Rev. 46, 828 - 828 (1934)
* W. Wang and A. Zunger, J. Phys. Chem. 98, 2158 (1994)
* W. Wang and A. Zunger, J. Chem. Phys. 100, 2394 (1994)
* [http://www.sst.nrel.gov/topics/nano/escan.html http://www.sst.nrel.gov/topics/nano/escan.html]