具有奇异M-矩阵结构的非线性特征值问题的正特征向量及其牛顿迭代解

提出具有不可约奇异M-矩阵结构的非线性特征值问题有唯一正特征向量的充分条件.研究表明任意一个正数都是非线性特征值问题的特征值,并且与这些特征值相对应的正特征向量是唯一的.同时,构建数值求解此正特征向量的牛顿迭代法,并给出其收敛性.数值实验表明该迭代法是有效的.

Positive eigenvector of nonlinear eigenvalue problems with singular M-matrix and Newton iterative solution

Some sufficient conditions are proposed such that nonlinear eigenvalue problem with irreducible singular M-matrix has a unique positive eigenvector.Studies show that any positive number is the eigenvalue of nonlinear eigenvalue problems and the positive eigenvector corresponding to the eigenvalue is unique.Meanwhile,the Newton iterative method is constructed for numerically solving such a positive eigenvector,and some convergence result on this iterarive method are established.Finally,a numerical example is presented to show that the algorithm is effective.