A numerical algorithm for computing the restricted singular value decomposition of matrix triplets

Abstract

An algorithm is developed for computing the restricted singular value decomposition (RSVD) of general matrix triplets. It consists of three stages: we first show that orthogonal transformations can be constructed to extract a regular triplet from a given general matrix triplet; after preprocessing the regular triplet, we reduce the problem to computing the ordinary singular value decomposition of a product of three upper triangular matrices having the same number of dimensions; then we apply the implicit Kogbetliantz technique to this matrix product. Other structural indices of the RSVD can be obtained by computing the ranks of certain submatrices. Numerical examples are provided to illustrate the accuracy of the algorithm.