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Constrained solutions of the eigenvalue problem in truncated basis sets
Author(s) -
Sadlej Andrzej J.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:1<35::aid-qua7>3.0.co;2-3
Subject(s) - orthogonality , eigenvalues and eigenvectors , eigenfunction , hermitian matrix , mathematics , basis (linear algebra) , simple (philosophy) , basis function , character (mathematics) , curse of dimensionality , divide and conquer eigenvalue algorithm , set (abstract data type) , mathematical analysis , pure mathematics , computer science , physics , geometry , quantum mechanics , philosophy , statistics , epistemology , programming language
It is shown that simple orthogonality constraints between some set of known approximate eigenfunctions and another set of functions which are to be determined as approximate eigensolutions need to be modified. The proposed modification introduces a measure of the approximate character of the known functions and leads to the reduction of the dimensionality of the eigenvalue problem for other solutions. The discussed method is fully variational and leads directly to a Hermitian eigenvalue problem. This approach is also independent of the choice of truncated basis sets for different classes of approximate solutions of the eigenvalue problem. © 1997 John Wiley & Sons, Inc.