We study the preconditioning of the augmented system formulation of the
least squares problem
, viz.
where A is a sparse matrix of order
to symmetrically precondition the system to obtain, after a simple block Gaussian elimination, the reduced symmetric quasi-definite (SQD) system
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We discuss the conditioning of the SQD system with some
minor extensions to standard eigenanalysis, show the difficulties associated
with
choosing the basis matrix
, and discuss how sparse direct techniques can
be used
to choose it. We also comment on the common case where A is an
incidence matrix
and the basis can be chosen graphically.