The stability of formulae of the Gohberg–Semencul–Trench type for Moore–Penrose and group inverses of Toeplitz matrices

We present a stability analysis of Gohberg–Semencul–Trench type formulae for the Moore–Penrose and group inverses of singular Toeplitz matrices. We develop a fast algorithm for the computation of the Moore–Penrose inverse based on a Gohberg–Semencul–Trench type formula and the LSQR method. For the g...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 498; pp. 117 - 135
Main Authors Xie, Pengpeng, Wei, Yimin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2016
Subjects
DGMRES
Group inverse
LSQR
Moore–Penrose inverse
Toeplitz matrix
DGMRES
Moore–Penrose inverse
15A22
65F15
Group inverse
LSQR
Toeplitz matrix
15A18
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Summary:We present a stability analysis of Gohberg–Semencul–Trench type formulae for the Moore–Penrose and group inverses of singular Toeplitz matrices. We develop a fast algorithm for the computation of the Moore–Penrose inverse based on a Gohberg–Semencul–Trench type formula and the LSQR method. For the group inverse, the DGMRES method is used to perform the fast computation. Numerical tests show that the fast algorithms designed here are at least as good as the known Newton iteration.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2015.01.029