A QR–method for computing the singular values via semiseparable matrices (original) (raw)

This paper presents a new method for computing the singular value decomposition (SVD) of a real matrix A via the use of upper triangular semiseparable (UTSS) matrices. The proposed algorithm first efficiently reduces A into a UTSS matrix through orthogonal transformations, allowing for accurate approximations of the largest singular values early in the process. Subsequently, an iterative method is developed to transform the UTSS matrix into a block diagonal form, which is equivalent to an implicit QR-iteration. The combined approach demonstrates computational efficiency and potential applications in various fields such as data mining and gene expression analysis.