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On the least squares procedure for atomic calculations
Author(s) -
Lloyd M. H.,
Delves L. M.
Publication year - 1969
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/qua.560030203
Subject(s) - least squares function approximation , mathematics , helium , convergence (economics) , matrix (chemical analysis) , quantum , physics , quantum mechanics , chemistry , statistics , chromatography , estimator , economics , economic growth
We discuss the properties of one version of the least squares ( LS ) method for the solution of the Schrödinger equation. These properties are exemplified by a number of calculations on the n 1 S and n 3 S states of helium, up to principal quantum number three, which are very much more accurate than previous LS calculations on helium. Particular attention is paid to the convergence properties of the LS procedure and we compare it with the simpler Rayleigh–Ritz ( RR ) procedure in the case when the RR matrix elements are evaluated numerically over the same quadrature mesh as used in the LS procedure. We conclude that although the LS procedure is capable of high accuracy it has no advantages which would justify its sole use in place of the RR procedure. However, it does have some advantages when used in conjunction with RR , in that it gives an estimate of the numerical accuracy of the RR energies.