RGSD an algorithm for computing the Kronecker structure and reducing subspaces of singular A-lB pencils
RGSD an algorithm for computing the Kronecker structure and reducing subspaces of singular A-lB pencils
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RGSD 一种计算 Kronecker 结构并减少奇异 A-1B 铅笔子空间的算法
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发表时间：
1986
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通讯作者：
B. Kågström
中科院分区：
文献类型：
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作者：
B. Kågström
本文提出了一种计算矩阵束A -λ B的Kronecker标准形（KCF）结构元素的算法（RGSVD），其中A和B是复m × n矩阵。RGSVD基于重复的广义奇异值分解（或更精确地说，分区正交矩阵的余弦-正弦分解）。它提取零和/或无限特征值的结构以及$A - lambda B$的左（行）或右（列）最小索引。通过累积等价变换，RGSVD还产生与例如零结构和右克罗内克指数相关联的约简子空间对。
An algorithm (RGSVD) for computing the structure elements associated with the Kronecker canonical form (KCF) of a matrix pencil $A - lambda B$, where A and B are complex m by n matrices, is presented. RGSVD is based on repeated generalized singular value decompositions (or more precisely cosine-sine decompositions of partitioned orthonormal matrices). It extracts the structures of the zero and/or the infinite eigenvalues together with the left (row) or right (column) minimal indices of $A - lambda B$. By accumulating equivalence transformations, RGSVD also produces pairs of reducing subspaces associated with e.g. the zero structure and the right Kronecker indices.