Fast diagonalisation of nonlocal pseudopotential Hamiltonians

X. Gonze, J. P. Vigneron, J. P. Michenaud

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The calculation of band structure and total energy of solids involves the search for the few lowest (M) eigenvectors and eigenvalues of large matrices (size N × N). Standard algorithms which diagonalise the matrix entirely scale as N3, while procedures for extracting only a subset of M eigenvalues and eigenvectors scale as MN2. Two methods are described which aim at finding the lowest eigenvalues and corresponding eigenvectors of a nonlocal pseudopotential Hamiltonian. Both approaches lead to an algorithm which scales roughly as MN4/3.

Original languageEnglish
Article number004
Pages (from-to)525-540
Number of pages16
JournalJournal of Physics Condensed Matter
Issue number3
Publication statusPublished - 1989
Externally publishedYes


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