Method of Continued Fractions for Solving Coupled Linear Equations
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概要
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The method of continued fractions (MCF) proposed by the author has turned out very efficient for solving a set of linear algebraic or integral equations. It has been used for solving the Faddeev equation of triton and ^3He. In the present article, I discuss the mathematical aspect of MCF: It generates a set of finite continued fractions, thus giving a mathematically exact solution of a given set of equations in the discretized space. For handling the continued fractions, two recurrence relations are proposed. It is shown that the MCF is robust for an ill-conditioned matrix. An example is given for the Hilbert matrix, for which the Gaussian elimination method fails already in a 20×20 matrix, while the MCF applied to the 200×200 matrix is quite robust. Only several iterations yield satisfactory convergence.
- 1996-04-15