Numerical Algorithms

, Volume 66, Issue 3, pp 609–641 | Cite as

An approximate eigensolver for self-consistent field calculations

Original Paper


In this paper, we give a comprehensive error analysis for an approximate solution method for the generalized eigenvalue problems arising for instance in the context of electronic structure computations based on density functional theory. The solution method has been demonstrated to excel as compared to established solvers in both computational effort and scaling for parallelization. Here we estimate the improvement provided by our proposed subspace method starting from the initial approximations for instance provided in the course of the self-consistent field iteration, showing that in general the approximation quality is improved by our method to yield sufficiently accurate eigenvalues.


Electronic structure computations Density functional theory Generalized eigenvalue problem Iterative diagonalization 

Mathematics Subject Classifications (2010)

65F15 65F08 65Z05 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

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