# Upper bound and stability of scaled pseudoinverses

@article{Wei1995UpperBA, title={Upper bound and stability of scaled pseudoinverses }, author={Musheng Wei}, journal={Numerische Mathematik}, year={1995}, volume={72}, pages={285-293} }

Summary.
For given matrices
$X$ and
$D$
where
$D$
is positive definite
diagonal, a weighed pseudoinverse of
$X$
is defined by
$X (D)^+ = (X^{\rm H} D^2 X)^+ X ^{\rm H} D^2$
and an oblique projection of
$X$ is defined by
$P (D) = XX (D)^+$
.
When
$X$ is of full column rank, Stewart [3] and
O'Leary [2] found sharp upper bound of oblique projections
$P (D)$
which
is independent of
$D$,
and an upper bound of weighed pseudoinverse
$X (D)^+$
by
using the bound of
$P(D)$.
In this paper we… CONTINUE READING

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