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Liu, Xiaoji; Jin, Hongwei; Yu, Yaoming

Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices. (English) Zbl 1283.65032

Linear Algebra Appl. 439, No. 6, 1635-1650 (2013).
Summary: The main aim of this paper is to provide a higher-order convergent iterative method in order to calculate the generalized inverse of a given matrix. We extend the iterative method proposed by W. Li and Z. Li [Appl. Math. Comput. 215, No. 9, 3433–3442 (2010; Zbl 1185.65057)] to compute the \(\{2\}\)-inverse, the generalized inverse \(A_{T,S}^{(2)}\), the \(\{2, 3\}\)-inverse and the \(\{2, 4\}\)-inverse. Moreover, we modify the iterative method to compute the generalized inverse \(A_{T,S}^{(2)}\) of Toeplitz matrices by using the displacement theory.

Cited in 24 Documents

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems

Keywords:

higher-order convergence; iterative method; generalized inverse \(A^{(2)}_{T,S}\); Toeplitz matrix; displacement theory

Citations:

Zbl 1185.65057
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\textit{X. Liu} et al., Linear Algebra Appl. 439, No. 6, 1635--1650 (2013; Zbl 1283.65032)
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References:

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