BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-89-03
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: The restricted singular value decomposition: properties and
               applications
        TYPE:: Manuscript
      AUTHOR:: De Moor, Bart L. R.
      AUTHOR:: Golub, Gene H.
        DATE:: April 1989
       PAGES:: 70
    ABSTRACT:: The restricted singular value decomposition (RSVD) is the
               factorization of a given matrix, relative to two other given
               matrices. It can be interpreted as the ordinary singular
               value decomposition with different inner products in row and
               column spaces. Its properties and structure are investigated
               in detail as well as its connection to generalized eigenvalue
               problems, canonical correlation analysis and other
               generalizations of the singular value decomposition.

               Applications that are discussed include the analysis of the
               extended shorted operator, unitarily invariant norm
               minimization with rank constraints, rank minimization in
               matrix balls, the analysis and solution of linear matrix
               equations, rank minimization of a partitioned matrix and the
               connection with generalized Schur complements, constrained
               linear and total linear least squares problems, with mixed
               exact and noisy data, including a generalized Gauss-Markov
               estimation scheme. Two constructive proofs of the RSVD in
               terms of other generalizations of the ordinary singular value
               decomposition are provided as well.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-89-03