10 - A qr-like svd algorithm for a product/quotient of several matrices

Abstract

This chapter derives a new algorithm for constructing unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and right transformations on the individual matrices and amounts to computing the generalized singular value decomposition of the sequence. The proposed algorithm is related to the classical Golub-Kahan procedure for computing the singular value decomposition of a single matrix in that it constructs a bidiagonal form of the sequence as an intermediate result. When applied to two matrices, this new method is an alternative way of computing the quotient and product singular value decomposition (SVD) and is more economical than current methods.