Generalized Singular Value Decompositions : A - - Proposal for a Standardized Nomenclature

An alphabetic and mnemonic system of names for several matrix decompositions related to the singular value decomposition is proposed: the OSVD, PSVD, QSVD, RSVD, SSVD, TSVD. The main purpose of this note is to propose a standardization of the nomenclature and the structure of these matrix decompositions. 1 I n t r o d u c t i o n . The ordinary singular value decomposition (OSVD) has become an important tool in the analysis and numerical solution of .numerous problems. Not only does it allow for an elegant problem formulation, but at the same time it provides geometrical and algebraic insight together with an immediate numerically robust implementation [lo]. It plays a prominent role in numerous *Research supported in part by the US-Army under contract DAAL03-87-K-0095 ‘Dr. De Moor is on leave from the Katholieke Universiteit Lenven, Belgium and is also with the Information Systems Lab, Department of Electrical Engineering, Stanford University. He is supported by an Adimmed Research Fellowship in Science and Technology of the NATO Science Fellowships Programme and a grant from IBM.