A trust region spectral method for large-scale systems of nonlinear equations

Meilan Zeng,Guanghui Zhou

doi:10.1186/s13660-016-1117-x

Abstract

The spectral gradient method is one of the most effective methods for solving large-scale systems of nonlinear equations. In this paper, we propose a new trust region spectral method without gradient. The trust region technique is a globalization strategy in our method. The global convergence of the proposed algorithm is proved. The numerical results show that our new method is more competitive than the spectral method of La Cruz et al. (Math. Comput. 75(255):1429-1448, 2006) for large-scale nonlinear equations.

Highlights

1 Introduction In this paper we introduce a trust region spectral method for solving large-scale systems of nonlinear equations
Many algorithms have been presented for solving the large-scale problem ( )
The purpose of this paper is to extend the spectral method for solving large-scale systems of nonlinear equations by using the trust region technique

Summary

Introduction

1 Introduction In this paper we introduce a trust region spectral method for solving large-scale systems of nonlinear equations Many algorithms have been presented for solving the large-scale problem ( ). The method uses the residual ±F(xk) as a search direction and the trial point at each iteration is xk – λkF(xk), where λk is a spectral coefficient. Conjugate gradient techniques have been developed for solving large-scale nonlinear equations (see [ – ]).

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Results

Conclusion