求实对称张量Z-特征值的牛顿法

Newton Method for Computing the Z-Eigenvalues of a Real Symmetric Tensor

文章提出一个求解实对称张量Z-特征值及特征向量的牛顿法.该方法将张量Z-特征值问题转化为等价的非线性方程组,并用牛顿法求解.经过改进的方向具有下降性,从而保证算法的全局及二阶收敛性.数值实验结果表明,算法有效.

In this paper,a Newton method is proposed for computing the Z-eigenvalues and corresponding ei-genvectors of a real symmetric tensors. The Z-eigenvalue problem is transformed into an equivalent system of nonlinear equations which is solved by Newton method. The modified direction is descent,which can en-sure the global and quadratic convergence of this algorithm. Some numerical results show that this method is effective.