Czechoslovak Mathematical Journal

, Volume 66, Issue 3, pp 859–879 | Cite as

Convergence of Rump’s method for computing the Moore-Penrose inverse



We extend Rump’s verified method (S.Oishi, K.Tanabe, T.Ogita, S.M.Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse.


Moore-Penrose inverse condition number ill-conditioned matrix 

MSC 2010

65F05 15A24 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamen, FujianP.R. China
  2. 2.School of Mathematics and Computer ScienceGuizhou Normal UniversityGuiyang, GuizhouP. R. China
  3. 3.School of Mathematical SciencesFudan UniversityShanghaiP.R. China
  4. 4.Shanghai Key Laboratory of Contemporary Applied MathematicsShanghaiP. R. China

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