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@MISC{,
            author = {Fassbender, H. and Rozložn{\'{\i}}k, Miroslav},
             title = {On the conditioning of factors in the SR decomposition},
           journal = {Linear Algebra and Its Applications},
              year = {2016},
          abstract = {Almost every nonsingular matrix A 2 R2m;2m can be decomposed into
the product of a symplectic matrix S and an upper J-triangular matrix
R. This decomposition is not unique. In this paper we analyze the free-
dom of choice in the symplectic and the upper J-triangular factors and
review several existing suggestions on how to choose the free parameters
in the SR decomposition. In particular we consider two choices leading
to the minimization of the condition number of the diagonal blocks in the
upper J-triangular factor and to the minimization of the conditioning of
the corresponding blocks in the symplectic factor. We develop bounds for
the extremal singular values of the whole upper J-triangular factor and
the whole symplectic factor in terms of the spectral properties of even-
dimensioned principal submatrices of the skew-symmetric matrix associ-
ated with the SR decomposition. The theoretical results are illustrated
on two small examples.},
  Preprint project = {NCMM},
     Preprint year = {2016},
   Preprint number = {04},
       Preprint ID = {NCMM/2016/04}
}