Self-correcting iterative methods for computing 2 -inverses

Stanimirović, Predrag S.

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 1, page 27-36
  • ISSN: 0044-8753

Abstract

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In this paper we construct a few iterative processes for computing { 2 } -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.

How to cite

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Stanimirović, Predrag S.. "Self-correcting iterative methods for computing ${2}$-inverses." Archivum Mathematicum 039.1 (2003): 27-36. <http://eudml.org/doc/249137>.

@article{Stanimirović2003,
abstract = {In this paper we construct a few iterative processes for computing $\lbrace 2\rbrace $-inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.},
author = {Stanimirović, Predrag S.},
journal = {Archivum Mathematicum},
keywords = {generalized inverses; Moore–Penrose inverse; error matrix; generalized inverses; Moore-Penrose inverse; error matrix},
language = {eng},
number = {1},
pages = {27-36},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Self-correcting iterative methods for computing $\{2\}$-inverses},
url = {http://eudml.org/doc/249137},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Stanimirović, Predrag S.
TI - Self-correcting iterative methods for computing ${2}$-inverses
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 1
SP - 27
EP - 36
AB - In this paper we construct a few iterative processes for computing $\lbrace 2\rbrace $-inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.
LA - eng
KW - generalized inverses; Moore–Penrose inverse; error matrix; generalized inverses; Moore-Penrose inverse; error matrix
UR - http://eudml.org/doc/249137
ER -

References

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  11. A self-correcting matrix iteration for the Moore-Penrose inverse, Linear Algebra Appl. 244 (1996), 357–363. (1996) MR1403289
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  14. Universal iterative methods for computing generalized inverses, Acta Math. Hungar. 79(3) (1998), 253–268. (1998) MR1616062
  15. Block representation of { 2 } , { 1 , 2 } inverses and the Drazin inverse, Indian J. Pure Appl. Math. 29 (1998), 1159–1176. (1998) MR1672776
  16. Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method, Linear Algebra Appl. 10 (1975), 163–175. (1975) Zbl0327.15012MR0416001
  17. The representations of the generalized inverses ( A ⊗ B ) T , S ( 1 , 2 ) and ( A ⊗ B ) T , S ( 2 ) and some applications, J. Shanghai Univ. (Natural Sciences) 24 (1995), 1–6. (1995) 
  18. Iterative refinement of generalized matrix inverses now practicable, SIGNUM Newsletter 13.4 (1978), 9–10. (1978) 
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  20. On computing the generalized inverse of a linear operator, Glasnik Matematički 2(22) No 2 (1967), 265–271. (1967) Zbl0149.35101MR0234967

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