Approximation of Matrices and a Family of Gander Methods for Polar Decomposition
Approximation of Matrices and a Family of Gander Methods for Polar Decomposition
复制标题
矩阵逼近和一族极坐标分解的 Gander 方法
DOI：
10.1007/s10543-006-0053-4
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发表时间：
2006
影响因子：
1.5
通讯作者：
K. Zietak
中科院分区：
文献类型：
--
作者：
B. Laszkiewicz;K. Zietak
考虑了两个矩阵逼近问题：次酉阵关于酉不变范数的逼近和关于谱范数的最小秩逼近。将Maher给出的关于方阵关于Schatten范数的次么正逼近的一个刻画推广到矩形矩阵和任意酉不变模的情形。基于Gander方法族和Higham极分解尺度法，提出了计算次么正逼近和最小秩近似值的迭代方法。详细研究了Gander方法的性质。
Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details.