A Modified Tensor Method For Singular Nonlinear Equations

Nonlinear equations has been a hot research scholars at home and abroad, this is because inengineering practice, economics, information security and other aspects of dynamics there are plentyof practical problems eventually transformed into nonlinear equations.In this paper, we study the modified tensor method for singular nonlinear equations (theJacobian matrix of the root is singular). The main idea of the modified tensor method is using thedifference of the Jacobian matrix to construct low-rank tensor model, thus to construct theapproximate linear model. The structure of this paper is organized as follows．The first chapter describes the origins and progress in research of tensor method for solvingnonlinear equations. The second chapter describes some basic knowledge of this article, thetheoretical knowledge and algorithms of the Newton method, the Levenberg-Marquard method, theQuasi-Newton method and the tensor method. The third chapter describes the modified tensormodel, based on this model a modified tensor algorithm is proposed for solving nonlinear equations.The convergence of the modified tensor algorithm is proved. In the fourth chapter, numerical resultsof the modified tensor method and the tensor method in reference [6] are reported and compared.Finally, this conclusion is given.