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