Convergence of Iterative Methods

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概要

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• 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 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. (Fig2). Then amore efficient iterative method (17), of which coefficient of convergency is expressed as (20), is presented, and its application to the variational technique is discussed. The method is shown to be convenient since no troublesome procedure solving the secular determinant is needed.

• 理論物理学刊行会の論文

著者

• Kikuta Takashi

  Department Of Physics Faculty Of Science University Of Tokyo

関連論文

• Effect of Hard Core on the Binding Energies of H^3 and He^3, I^*
• Extensions of Variational Methods, II : Two Parameter Eigenvalue Problem for the Deuteron State
• Convergence of Iterative Methods
• Extensions of Variational Methods, I : Super-Stationary Variational Method

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