T. Zhanlav, O. Chuluunbaatar and G. Ankhbayar, “Relationship between the Inexact Newton Method and the Continuous Analogy of Newton Method,” Revue D’Analyse Numerique et de Theorie de L’Approximation, Vol. 40, No. 2, 2011, pp. 182-189.

has been cited by the following article:

• TITLE: The Continuous Analogy of Newton’s Method for Solving a System of Linear Algebraic Equations

  AUTHORS: Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Gantumur Ankhbayar

  KEYWORDS: Continuous Analogy of Newton’s Method; Solving the System of Linear Algebraic Equations; Convergence; Choice of Iteration Parameter

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1A, January 30, 2013

  ABSTRACT: We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.