# Overview¶

This is document for the sample program which uses K \(\omega\) library in the ISSP Math Library; this program computes the Green’s function with \(K\omega\). For the details of K \(\omega\) library, See “\(K\omega\) manual” in this package.

## Calculation in this program¶

This program compute the Green’s function

where \(| i \rangle\) is a wavefunction, \({\cal H}\) is the Hamiltonian, and \(z\) is a complex frequency.

- \({\cal H}\) in the above equation is obtained by either the
following two ways:

Input \({\cal H}\) as a file with the MatrixMarket format

Construct \({\cal H}\) as a Hamiltonian of the Heisenberg model in this program.

In the computation of the Green’s function, we use either the following two method according to the type of \({\hat H}\) (a real- or a complex- number).

\({\hat H}\) of real numbers : Shifted Bi-Conjugate Gradient(BiCG) method

\({\hat H}\) of complex numbers : Shifted Conjugate Orthogonal Conjugate Gradient(COCG) method