摘要
首先证明了矩阵方程Ｘ＋ ＡＴＸ－ １ Ａ＝ Ｉ的最大解是十分良态的，然后给出了２ 种求解最大解的迭代方法，并且讨论了这些方法的收敛性。这２ 种方法，一种是线性收敛的，其优点是迭代过程不需要求矩阵的逆；另一种是二次收敛的，数值试验的结果表明该方法在计算速度和精度方面都明显地优于现有的其他几种迭代方法。
An elegant property of the maximal solution to the matrix equation X+A T X -1 A=I is presented.The property shows that the maximal solution is well\|conditioned.Two new iteration methods for finding the maximal solution are proposed.Of these two methods,one is a linearly convergent iteration without matrix inversion,and one is related to Newton's method and quadratically convergent.The convergence analysis is also given.Comparisons have been made with other known methods.In all test problems the new quadratically convergent method appeared to be far superior to the other methods.
出处
《北京大学学报（自然科学版）》
CAS
CSCD
北大核心
2000年第1期29-38,共10页
Acta Scientiarum Naturalium Universitatis Pekinensis
基金
国家自然科学基金
关键词
矩阵方程
最大解
数值方法
matrix equation
maximal solution
numerical methods
