| The higher order tensor is multidimensional linear mapping. It’s a generalization of matrices. A matrix is a twice order tensor. In this thesis, a Newton method is proposed for computing the Z- eigenvalues and corresponding eigenvectors of real symmetric tensors. The Zeigenvalue problem is transformed into an equivalent system of nonlinear equations which is solved by Newton method.This thesis mainly discusses the Newton algorithms and theories, which is a quite different method compared before to solve eigenvalues and corresponding eigenvectors of a real symmetric tensor. The improvement we made is to design the descent direction and global technic which can help us to prove the global and quadratic convergence. We report the numerical experiments of this and other methods. It shows the effectiveness of our method.The structure of this thesis is organized as follows. The first Chapter describes the origins and progress in research of solving Z- eigenvalues of real symmetric tensors. The second Chapter describes some basic knowledge of this article. The theoretical knowledge and algorithm of Newton method are included. In the third Chapter, we propose a model of nonlinear equations, discuss the algorithm of Newton method and corresponding strategy and prove the global convergence. In the fourth Chapter, the numerical results of the Newton method, power method and shifted power method are reported and compared with each other. Finally, the conclusion is given. |
