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

Yunkun Chen; Xinghua Shi; Yi Min Wei

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 3, page 859-879
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Chen, Yunkun, Shi, Xinghua, and Wei, Yi Min. "Convergence of Rump's method for computing the Moore-Penrose inverse." Czechoslovak Mathematical Journal 66.3 (2016): 859-879. <http://eudml.org/doc/286842>.

@article{Chen2016,
abstract = {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.},
author = {Chen, Yunkun, Shi, Xinghua, Wei, Yi Min},
journal = {Czechoslovak Mathematical Journal},
keywords = {Moore-Penrose inverse; condition number; ill-conditioned matrix},
language = {eng},
number = {3},
pages = {859-879},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of Rump's method for computing the Moore-Penrose inverse},
url = {http://eudml.org/doc/286842},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Chen, Yunkun
AU - Shi, Xinghua
AU - Wei, Yi Min
TI - Convergence of Rump's method for computing the Moore-Penrose inverse
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 859
EP - 879
AB - 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.
LA - eng
KW - Moore-Penrose inverse; condition number; ill-conditioned matrix
UR - http://eudml.org/doc/286842
ER -

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