Spectrum folding
The term Folded Spectrum Method (FSM) or spectrum folding describes a mathematical iterative optimization method for eigenvalue problems . With it it is possible to determine the eigenvector of a large eigenvalue problem for the matrix that is closest to any target eigenvalue (from the middle of the spectrum ) without having to solve the entire matrix .
formula
, with and the identity matrix .
rating
In contrast to the mountain climbing algorithm (English hill climbing , also downhill ) or the CG method , the gradient here (FSM) is determined by applying the matrix twice :
This method is particularly suitable for large, thinly populated matrices .
literature
- JKL MacDonald: On the Modified Ritz Variation Method. In: Physical Review. 46, 1934, p. 828.
- LW Wang, A. Zunger: Electronic Structure Pseudopotential Calculations of Large (.apprx. 1000 Atoms) Si Quantum Dots. In: Journal of Chemical Physics. 98, 1994, p. 2158. doi: 10.1021 / j100059a032
- LW Wang, A. Zunger: Solving Schrodinger's equation around a desired energy: Application to silicon quantum dots. In: Journal of Chemical Physics. 100, 1994, p. 2394.