On the Convergence Speed for a Class of Interactive Methods

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概要

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• We derived two of iterative methods, each containing two parameters and having cubic convergence for the zeros of all sufficiently regular functions. Our mehtods include Laguerre's, Ostrowski's, Halley's and Hansen and Patrick's methods. We established that our methods converge globally and monotonically to the real zeros of the said functions by using the said methods, we established that as to the convergence speed, Ostrowski's method is the fastest, Halley's mehtod is the slowest and our mehtods excepting the said two mehods are intermediate. In this paper, we discuss the convergence speed in one of the said two types of our methods are intermediate. In this paper, we discuss the convergence speed in one of the said two types of our methods. Here, in the case where one of the two parameters contained in the said type of methods is given, we show how to derive the fastest method by the suitable choice of the other parameter.

• 一般社団法人情報処理学会の論文
• 1994-08-15

著者

• Ohtani Koji

  Information Processing Center Kobe University Of Mercantile Marine

• Murakami Takahiko

  Department of Mathematics, Kobe University of Mercantile Marine

• Murakami Takahiko

  Department Of Mathematics Kobe University Of Merantile Marine

関連論文

• On the Convergence Speed for a Class of Interactive Methods
• Some Fifth Order Multipoint Iterative Formulae for Solving Equations
• A Class of Fifth Order Multipoint Iterative Methods for the Solution of Equations
• On the Attainable Order of Convergence for Some Multipoint Iteration Functions
• On Some Iterative Formulas for Solving Nonlinear Scalar Equations
• On the Global Convergence of Some Iterative Formulas
• On the Convergence Speed for Some Iterative Methods
• On the Global Convergence of Some Iterative Formulas

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