Folded spectrum method
Encyclopedia
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
. This means you can get a vector 
in the middle of the spectrum without solving the matrix.
, with 
and 
the Identity matrix
.
In contrast to the Conjugate gradient method
, here the gradient calculates by twice multipling matrix
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
for solving large eigenvalue problems.
Here you always find a vector with an eigenvalue close to a search-value
. This means you can get a vector in the middle of the spectrum without solving the matrix. , with and the Identity matrixIdentity matrix
In linear algebra, the identity matrix or unit matrix of size n is the n×n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context...
.
In contrast to the Conjugate gradient method
Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too...
, here the gradient calculates by twice multipling matrix
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