Prog. Theor. Phys. Vol. 10 No. 6 (1953) pp. 653-672
Convergence of Iterative Methods
Department of Physics, University of Tokyo
(Received October 31, 1953)
For various iterative methods in eigenvalue problem which are used to solve the bound states and scattering problems, we introduce the coefficient of convergency which indicates not only the convergency condition when the iteration is performed endlessly, but also the efficiency of successive approximation for any finite step. In this way the convergency properties of these iterative methods are investigated from a common stand-point, though the main new results stated in this paper concern the scattering problems. Comparing the convergence properties for Schwinger's iterative method and Born's successive approximation in scattering problem, we show the former is considerably superior in low energy domain, while in high energies the latter is more favourable by its simplicity. (Fig 2).
Then a more efficient iterative method (17), of which coefficient of convergency is expressed as (20), is presented, and it application to the variational technique is discussed. The method is shown to be convenient since no troublesome procedure solving the secular determinant is needed.
DOI : 10.1143/PTP.10.653
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Citing Article(s) :
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Upper and Lower Bounds of Born Approximation, II
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Effects of the Coulomb Repulsion on the Electro-Magnetic Radii of H3 and He3 Nuclei