A probing method is presented to find the diagonal of the inverse of a sparse, diagonal dominant, matrix. First, some properties of the matrix inverse are established. This suggests several ways to determine effective probing vectors. An iterative method is then applied to solve the resulting sequence of linear systems, from which the diagonal of the matrix inverse is extracted.
The algorithm is applied to the solution of Dyson's equation in Dynamic Mean Field Theory (DMFT). DMFT has recently emerged as a very powerful and reliable tool in physics for the investigation of lattice models of correlated electrons in a quantum many-body system.