RGSVD—AN Algorithm for Computing the Kronecker Structure and Reducing Subspaces of Singular $A - \lambda B$ Pencils
SIAM Journal on Scientific and Statistical ComputingPublished 1 January 1986
Bo Kågström
Citations57
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Abstract
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.
Keywords
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