Folded spectrum method explained

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 1 ) ^{2} \Psi _{i} , with 0 <\alpha < 1 and 1 the Identity matrix.

In contrast to the Conjugate gradient method, here the gradient calculates by twice multiplying matrix

H: G\sim H → G\sim H ^{2.}

Literature

• MacDonald . J. K. L. . On the Modified Ritz Variation Method . Physical Review . American Physical Society (APS) . 46 . 9 . 1934-11-01 . 0031-899X . 10.1103/physrev.46.828 . 828. 1934PhRv...46..828M .
• Wang . Lin Wang . Zunger . Alex . Electronic Structure Pseudopotential Calculations of Large (.apprx.1000 Atoms) Si Quantum Dots . The Journal of Physical Chemistry . American Chemical Society (ACS) . 98 . 8 . 1994 . 0022-3654 . 10.1021/j100059a032 . 2158–2165.
• Wang . Lin‐Wang . Zunger . Alex . Solving Schrödinger's equation around a desired energy: Application to silicon quantum dots . The Journal of Chemical Physics . AIP Publishing . 100 . 3 . 1994 . 0021-9606 . 10.1063/1.466486 . 2394–2397. 1994JChPh.100.2394W .
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