Memoirs of the Faculty of Science, Shimane University

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Memoirs of the Faculty of Science, Shimane University 25
1991-12-25 発行

統計的検定法の見地からのニュートン法の修正

A Modification of the Newton Method from a Viewpoint of Statistical Testing Methods
Morita, Tsukuo
Eguchi, Shinto
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Description
The Newton method has quitely universal use for a nonlinear optimization problem,max{ f(x) : x ∈U } . The algorithm satisfies to be quadratically convergent under a mildcondition. This paper concentrates on the further convergence from a statistical viewpoint.A deformation of the objective function f is proposed by association with methods of statisticaltesting hypothesis. It is shown that the k-step modified function enjoys convergence of(k + 2)-th order.