A completely rank revealing quotient URV decomposition

Abstract

This paper introduces a completely rank revealing complete orthogonal quotient decomposition for a pair of rectangular matrices. It reliably reveals an approximation of the minimum distance from a matrix pair with a prescribed quotient SVD structure. The approximation gives the yes minimum distance up to a small constant factor that is independent of the sizes of the matrices. Consequently the decomposition is well suited to the recovery of the non-generic quotient SVD structure of a pair of matrices that have been corrupted by errors. The use of a completely rank revealing decomposition is shown to improve estimates of matrix range space intersections for a system identification problem. Show more