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

Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Gantumur Ankhbayar

School of Mathematics and Computer Science, National University of Mongolia, Ulan-Bator, Mongolia.
School of Mathematics and Computer Science, National University of Mongolia, Ulan-Bator, Mongolia&Joint Institute for Nuclear Research, Dubna, Moscow region, Russia.

DOI: 10.4236/am.2013.41A032                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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