Studied Hermitian Positive Definite(HPD) Solutions of Three Classes of Nonlinear Matrix Equations 三类非线性矩阵方程的Hermitian正定解研究
This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems. 本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形,给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。
In chapter 2, we sets up the convergence theory of the alternating method for solving Hermitian positive definite systems of linear equations, and establishes the corresponding comparison theorem on its asymptotic convergence rate. 第二章首先介绍当系数矩阵是Hermitian正定矩阵时经典交替迭代法的收敛理论和相应的比较理论,同时我们给出了当分裂不同时对迭代渐进收敛率的影响。
Let A be a complex nonsingular matrix and an induced matrix Cm ( A ) be normal, Hermitian, positive definite and skew-Hermitian. The conditions under which A has these properties are discussed. 设A是复可逆矩阵,巨Cm(A)分别是正规的、厄米特的、正定的和反厄米特的,讨论A具有的性质的条件;
For positive definite Hermitian matrices A and B, we obtain an upper and a lower bound for the eigenvalues of AB in terms of those of A and B, which improve the results in [ 3 ]. 本文绘出了当A,B是正定Hermitian矩阵时,乘积AB的特征值的上、下界估计。所得结果改进了文[3]中相应结论。