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 数学进展 - 2016, Vol. 45(6): 939-954
 研究论文
 求解非对称线性方程组的不完全广义最小向后扰动法 An Incomplete Generalized Minimum Backward Perturbation Algorithm for Large Nonsymmetric Linear Systems 孙 蕾 SUN Lei 南京航空航天大学金城学院, 南京, 江苏, 210012 Jincheng College of Nanjing University of Aeronautics and Astronautics, Nanjing,Jiangsu, 210012, P. R. China 收稿日期: 2015-06-11 出版日期: 2016-11-10 2016, Vol. 45(6): 939-954 DOI: 10.11845/sxjz.2015119b
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Abstract：This paper gives the truncated version of the generalized minimum backward error algorithm (GMBACK)---the incomplete generalized minimum backward perturbation algorithm (IGMBACK) for large nonsymmetric linear systems. It is based on an incomplete orthogonalization of the Krylov vectors in question, and gives an approximate or quasi-minimum backward perturbation solution over the Krylov subspace. Theoretical properties of IGMBACK including finite termination, existence and uniqueness are discussed in details, and practical implementation issues associated with the IGMBACK algorithm are considered. Numerical experiments show that, the IGMBACK method is usually more efficient than GMBACK and GMRES, and IGMBACK, GMBACK often have better convergence performance than GMRES. Specially, for sensitive matrices and right-hand sides being parallel to the left singular vectors corresponding to the smallest singular values of the coefficient matrices, GMRES does not necessarily converge, and IGMBACK, GMBACK usually converge and outperform GMRES.
 PACS: O241.6

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