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