Modification of the DIIS method for diagonalizing large matrices

Hanchul Kim, Byung Deok Yu, Jisoon Ihm

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The existing 'residual minimization/direct inversion in the iterative subspace' (DIIS) method for the iterative calculation of low-lying eigenstates of a large matrix is further developed and modified. The DIIS method, which uses the residual minimization criterion, may fail to provide correct low-lying eigenspectra in the case of ill-formed matrices, e.g. the momentum-space representation of Hamiltonian matrices of systems containing transition metal, rare earth, or first-row elements. We suggest the inclusion of another criterion-the vanishing of the overlap integral of an iterative eigenvector with already obtained low-lying eigenvectors in order to prevent the eigenvector from collapsing to lower states. Two numerical examples of the success of our modified DIIS method in contrast to the failure of the conventional DIIS method are presented.

Original languageEnglish
Article number015
Pages (from-to)1199-1204
Number of pages6
JournalJournal of Physics A: Mathematical and Theoretical
Issue number4
StatePublished - 1994


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