关于近似极因子

ON THE APPROXIMATE POLAR FACTORS

易知这时H>0(表示H是正定矩阵),并且分解(1)中的Q与H是唯一确定的. 由于极分解在控制论与统计分析等领域中的应用,有关的计算方法与理论分析已经发展起来。 为了计算A的极因子Q与H,通常是先算出Q的近似解X。

To compute the polar decomposition A=QH, usually an approximate unitaryfactor X of A is first computed, and then the matrix K-1/2(X^HA+A^HX) is takenas an approximate Hermitian factor of A. This paper introduces the residual R=A-XK, and gives an approximate analysis of the approximate polar factors K andX.