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.