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Iterative calculation of eigenvalues and eigenvectors of large, real matrix systems with overlap
Author(s) -
Gallup G. A.
Publication year - 1982
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540030202
Subject(s) - eigenvalues and eigenvectors , eigenvalues and eigenvectors of the second derivative , eigenvalue perturbation , modal matrix , defective matrix , matrix differential equation , mathematics , spectrum of a matrix , matrix (chemical analysis) , iterative method , algorithm , mathematical analysis , diagonalizable matrix , symmetric matrix , physics , chemistry , quantum mechanics , chromatography
An improved method for obtaining a few eigenvalues and eigenvectors of the symmetric matrix system is presented:\documentclass{article}\pagestyle{empty}\begin{document}$$(A - \lambda S)c = 0$$\end{document} where S ≠ I . The method allows us to handle larger systems more easily than any other known to the author. It requires the inversion of S , and N 3 step, but thereafter each eigenvector and eigenvalue is obtained in a length of time proportional to N 2 . The relation of this method to the MOR and MMOR methods developed recently for handling the case, S = I , is discussed.