The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices

Keywords

Eigenvalues and eigenvectors, Laves phase, Density functional theory, Consistency (knowledge bases), Thermodynamics

References

• Simultaneous linear equations and the determination of eigenvaluesL. J. Paige, Olga Taussky — 1955
• An iterative method for finding characteristic vectors of a symmetric matrixWilliam Karush — 1951
• Algorithm for Diagonalization of Large MatricesR. K. Nesbet — 1965
• The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large symmetric matricesIsaiah Shavitt, Charles F. Bender, A. Pipano — 1973
• Theoretical study of curve crossing: ab initio calculations on the four lowest 1Σ+ states of LiFLuis R. Kahn, P. Jeffrey Hay, Isaiah Shavitt — 1974
• Studies in Configuration Interaction: The First-Row Diatomic HydridesCharles F. Bender, Ernest R. Davidson — 1969
• A new method for large-scale Cl calculationsB. Roos — 1972
• Modification of Nesbet's algorithm for the iterative evaluation of eigenvalues and eigenvectors of large matricesIsaiah Shavitt — 1970
• Computational Methods of Linear Algebra.D. J. Lewis, D. K. Faddeev, V. N. Faddeeva — 1966
• The solution of natural frequency equations by relaxation methodsJ. L. B. Cooper — 1948
• An iteration method for the solution of the eigenvalue problem of linear differential and integral operatorsCornelius Lanczos — 1950
• An iterative method for the solution of the eigenvalue problem of linear differential and integral1950

Cited by

• Configuration space truncation scheme for Hubbard HamiltonianM. A. H. Ahsan, C. R. Sarma — 1994
• Vertical spectrum of the C2H 2+ system. An open shell (SC)2‐CAS‐SDCI studyJ. Pitarch‐Ruiz, J. Sánchez‐Marín, Daniel Maynau — 2003
• An iterative method to solve the algebraic eigenvalue problemEmili Besalú, Ramon Carbó‐Dorca — 1997
• Linear response functions for a vibrational configuration interaction state.武久 小寺 — 2006
• Theoretical study of the double Renner effect for A2Pi MgNC/MgCN: higher excited rovibrational states.S. H. Katz, Horace C. Porter — 2007
• Co-operative sensor localization using maximum likelihood estimation algorithmUpendra Kumar Sahoo — 2008
• Nonadiabatic excited-state molecular dynamics modeling of photoinduced dynamics in conjugated molecules.Abdul Rahim Abdul Rahman, Abdul Rahim — 2011
• Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers.Michèle Tomasi — 2011
• The relativistic polarization propagator for the calculation of electronic excitations in heavy systems.John Julius Boekorsjom, Irwan Abdullah — 2014
• Vibrational anharmonicity of small gold and silver clusters using the VSCF method.Kamila Mizera — 2016
• Simulation ab initio des propriétés optiques des matériaux photoluminescents et apports méthodologiques dans le cadre d'une approche de cluster environnéFlorent Réal — 2006
• An Improved Lower Bound to the Ground-State Energy.Ignacio Jericó Bermejo — 2019
• Preconditioned techniques for large eigenvalue problemsKesheng Wu — 1997
• A block Rayleigh quotient iteration with local quadratic convergence.Jean‐Luc Fattebert — 1998
• Dynamic Restarting Schemes for Eigenvalue ProblemsKesheng Wu, Horst D. Simon — 1999
• Potential Flow Theory and Operation Guide for the Panel Code PMARCDale L. Ashby — 1999
• On the Subspace Projected Approximate Matrix methodJan Brandts, Ricardo Reis da Silva — 2011
• Subspace methods for sparse eigenvalue problemsBernhard Steffen — 2000
• Defects in strongly correlated and spin-orbit entangled quantum matterM. Becker — 2015
• Spectral portrait for non-hermitian large sparse matricesJean-François Carpraux, Jocelyne Erhel, Miloud Sadkane — 1994

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