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###

Further Details:
Error Bounds for Linear Equality Constrained Least Squares Problems

In this subsection, we will summarize the available error bound.
The reader may also refer to [2,13,18,50] for
further details.

Let
be the solution computed by the driver xGGLSE (see subsection
4.6). It is normwise
stable in a mixed forward/backward sense [18,13].
Specifically,
,
where
solves
,
and

*q*(*m*,*n*,*p*) is a modestly growing function of *m*, *n*, and *p*.
We take *q*(*m*,*n*,*p*) = 1 in the code fragment above.
Let
denote the Moore-Penrose pseudo-inverse of *X*.
Let
( = `CNDAB` above) and
( = `CNDBA` above)
where
and
.
When
is small, the error
is bounded by

When *B* = 0 and *d* = 0, we essentially recover error bounds for the
linear least squares (LS) problem:

where
.
Note that
the error in the standard least squares problem provided in section 4.5.1 is

since
.
If one assumes
that
*q*(*m*,*n*) = *p*(*n*) = 1, then the bounds are essentially the same.

** Next:** General Linear Model Problem
** Up:** Linear Equality Constrained Least
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*Susan Blackford*

*1999-10-01*