Folded spectrum method

Template:Short description 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 $\epsilon$. This means you can get a vector $\mathrm{\Psi }$ in the middle of the spectrum without solving the matrix.

${\mathrm{\Psi }}_{i+1}={\mathrm{\Psi }}_i-\alpha (H-\epsilon \mathrm{𝟏}{)}^2{\mathrm{\Psi }}_i$, with $0<{\alpha }^{}<1$ and $\mathrm{𝟏}$ the Identity matrix.

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

Literature

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

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