【摘要】 本文针对系数矩阵为方阵的非线性二次矩阵方程AX2+BX+C=0,结合多分裂法及牛顿法,给出了二次矩阵方程的两种迭代算法。同时,运用积分中值定理,对所得算法的收敛性进行了分析,得到相应算法的收敛性定理。最后,通过数值示例,对文中论述进行了强有力的验证。更多还原

【Abstract】 We analyze the problem of the computation of the nonlinear quadratic matrix equation(QME) AX2+BX+C=0,where A,B and C are square matrices.We propose a technique based on parallel multisplitting methods,and show how to incorporate Newton’s method into it.Also we give a local convergence theorem by making use of the integral mean-value theorem.Numerical experiments validate the effectiveness of this algorithm.更多还原