島根大学理学部紀要

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島根大学理学部紀要 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
森田 築雄
江口 真透
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内容記述(抄録等)
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.