mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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_= \Psi_i-\alpha( H- \varepsilon \mathbf )^2 \Psi_i

, with

0<\alpha^<1

and

\mathbf

the

Identity matrix In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial o ...

. In contrast to the

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 positive-definite. The conjugate gradient method is often implemented as an iterativ ...

, here the gradient calculates by twice multiplying matrix

H:\;G\sim H\rightarrow G\sim H^2.

Literature

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https://web.archive.org/web/20070806144253/http://www.sst.nrel.gov/topics/nano/escan.html
Numerical linear algebra {{Linear-algebra-stub