摘要
给出了一种求解广义Sylvester方程AXB-X+Q=0和AX-XB+Q=0的方法——级数截断方法。在级数截断方法中考虑了一个矩阵级数∑∞i=0AiQBi的截断,然后证明了这种方法的二次收敛性并给出了3个相应的算法。最后通过求解2个广义Sylvester方程的数值例子来说明了此方法的优越性。
In this paper we investigate a method for solving the general Sylvester equationsAXB-X＋Q=0 and AX-XB＋Q=0,which is called series truncation method.In this method we consider a truncation of the matrix series ∞∑i=0A^iQB^i,then prove its quadratic convergence and give three corresponding al gorithms.Finally we test its effectiveness by solving two general Sylvester equations.
出处
《丽水学院学报》
2007年第5期25-28,共4页
Journal of Lishui University
关键词
广义Sylvester方程
数列截断
二次收敛
特征值分解
谱半径
general sylvester equation
series truncation
quadratic convergence
eigenvalue decomposition
spectral radius
