BIT Numerical Mathematics

, Volume 13, Issue 2, pp 217–232

Perturbation theory for pseudo-inverses


  • Per-Åke Wedin
    • Institute of Computer sciences

DOI: 10.1007/BF01933494

Cite this article as:
Wedin, P. BIT (1973) 13: 217. doi:10.1007/BF01933494


A perturbation theory for pseudo-inverses is developed. The theory is based on a useful decomposition (theorem 2.1) ofB+ -A+ whereB andA arem ×n matrices. Sharp estimates of ∥B+ -A+∥ are derived for unitary invariant norms whenA andB are of the same rank and ∥B -A∥ is small. Under similar conditions the perturbation of a linear systemAx=b is studied. Realistic bounds on the perturbation ofx=A+b andr=b=Ax are given. Finally it is seen thatA+ andB+ can be compared if and only ifR(A) andR(B) as well asR(AH) andR(BH) are in the acute case. Some theorems valid only in the acute case are also proved.

Download to read the full article text

Copyright information

© BIT Foundations 1973