Volume 16, Issue 4
IMinpert: An Incomplete Minimum Perturbation Algorithm for Large Unsymmetric Linear Systems

L. Sun, X. H. Wang & Y. Guan

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Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 300-312

Published online: 2007-11

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  • Abstract

This paper gives the truncated version of the Minpert method: the incomplete minimum perturbation algorithm (IMinpert). It is based on an \emph{incomplete orthogonalization} of the Krylov vectors in question, and gives a quasi-minimum backward error solution over the Krylov subspace. In order to make the practical implementation of IMinpert easy and convenient, we give another approximate version of the IMinpert method: A-IMinpert. Theoretical properties of the latter algorithm are discussed. Numerical experiments are reported to show the proposed method is effective in practice and is competitive with the Minpert algorithm.

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@Article{NM-16-300, author = { L. Sun, X. H. Wang and Y. Guan}, title = {IMinpert: An Incomplete Minimum Perturbation Algorithm for Large Unsymmetric Linear Systems}, journal = {Numerical Mathematics, a Journal of Chinese Uniersities}, year = {2007}, volume = {16}, number = {4}, pages = {300--312}, abstract = { This paper gives the truncated version of the Minpert method: the incomplete minimum perturbation algorithm (IMinpert). It is based on an \emph{incomplete orthogonalization} of the Krylov vectors in question, and gives a quasi-minimum backward error solution over the Krylov subspace. In order to make the practical implementation of IMinpert easy and convenient, we give another approximate version of the IMinpert method: A-IMinpert. Theoretical properties of the latter algorithm are discussed. Numerical experiments are reported to show the proposed method is effective in practice and is competitive with the Minpert algorithm.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8058.html} }
TY - JOUR T1 - IMinpert: An Incomplete Minimum Perturbation Algorithm for Large Unsymmetric Linear Systems AU - L. Sun, X. H. Wang & Y. Guan JO - Numerical Mathematics, a Journal of Chinese Uniersities VL - 4 SP - 300 EP - 312 PY - 2007 DA - 2007/11 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/nm/8058.html KW - AB - This paper gives the truncated version of the Minpert method: the incomplete minimum perturbation algorithm (IMinpert). It is based on an \emph{incomplete orthogonalization} of the Krylov vectors in question, and gives a quasi-minimum backward error solution over the Krylov subspace. In order to make the practical implementation of IMinpert easy and convenient, we give another approximate version of the IMinpert method: A-IMinpert. Theoretical properties of the latter algorithm are discussed. Numerical experiments are reported to show the proposed method is effective in practice and is competitive with the Minpert algorithm.
L. Sun, X. H. Wang & Y. Guan. (1970). IMinpert: An Incomplete Minimum Perturbation Algorithm for Large Unsymmetric Linear Systems. Numerical Mathematics, a Journal of Chinese Uniersities. 16 (4). 300-312. doi:
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