International Symposium on Nonlinear Theory and its Applications


Session Number:A2L-F



A Representation by Power Series for the Sequence Generated by the Simplified Newton’s Method

Takashi Ozeki,  


Publication Date:2008/9/7

Online ISSN:2188-5079


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We discuss a property of the sequence of approximations obtained by the simplified Newton’s method. In the case of nonlinear functions with one variable, it has been proved that approximations of the simplified Newton’s method can be represented by a power series. Therefore, the convergence of the sequence can be accelerated by the ε algorithm and others. In this paper, we try to extend the result to several variables. It is shown that approximations of the simplified Newton’s method for several variables can be represented in the same way of one variable if those eigenvalues don’t idempotent each other. Moreover, in the case of more than two variables, we show exceptions that can’t be represented by any power series with constant vectors.