Numerische Mathematik

, Volume 72, Issue 2, pp 285–293 | Cite as

Upper bound and stability of scaled pseudoinverses

  • Musheng Wei


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 discuss the sharp upper bound of\(X (D)^+\) over a set\(D_+\) of positive diagonal matrices which does not depend on the upper bound of \(P(D)\), and the stability of\(X(D)^+\) over \(D_+\).

Mathematics Subject Classification (1991):15A09, 65F35 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Musheng Wei
    • 1
  1. 1.Department of Mathematics, East China Normal University, Shanghai 200062, China CN

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