The Green’s function ADC(2) has long proved to be a successful method for the study of dense double ionization spectra of molecules and clusters. This paper focuses on the computational aspects of the method, illustrating in particular the algorithms it entails in the context of subspace iteration techniques to compute eigenvalues and eigenvectors, and how these can be efficiently implemented. It is shown that, as in direct-CI procedures, the key matrix-multiply operation is effectively reduced to a number of smaller cache-size operations with matrix blocks built on-the-fly from the two-electron integrals, which can be implemented through fast basic linear algebra routines. Some parallelization aspects and specific diagonalization procedures are briefly discussed.