An improved Schulz-type iterative method for matrix inversion with application

In this paper, we present an algorithm which could be considered an improvement to the well-known Schulz iteration for finding the inverse of a square matrix iteratively. The convergence of the proposed method is proved and its computational complexity is analysed. The extension of the scheme to gen...

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Bibliographic Details
Published inTransactions of the Institute of Measurement and Control Vol. 36; no. 8; pp. 983 - 991
Main Authors Haghani, F Khaksar, Soleymani, F
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.12.2014
Sage Publications Ltd
Subjects
Algorithms
Computation
Convergence
Inverse
Inversions
Iterative methods
Matrix
Preconditioning
Sparse matrices
outer inverse
Sparse matrices
approximate inverse
preconditioner
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Summary:In this paper, we present an algorithm which could be considered an improvement to the well-known Schulz iteration for finding the inverse of a square matrix iteratively. The convergence of the proposed method is proved and its computational complexity is analysed. The extension of the scheme to generalized outer inverses will be treated. In order to validate the new scheme, we apply it to large sparse matrices alongside the application to preconditioning of practical problems.
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ISSN:0142-3312
1477-0369
DOI:10.1177/0142331214528350