| 非对称线性方程组的广义拟最小向后误差算法 |
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| 引用本文： | 魏红霞.非对称线性方程组的广义拟最小向后误差算法[J].南京航空航天大学学报(英文版),2000,17(2). |
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| 作者姓名： | 魏红霞 |
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| 作者单位： | 中国人民解放军国际关系学院计算中心南京,210039 |
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| 摘 要： | 正交投影方法已经广泛应用于求解线性方程组.人们很少注意到斜投影方法,事实上斜投影方法更适合于解大型非对称线性方程组.本文的目的是考虑一标准来判断是否一个给定的近似值是合适的,并给出一个算法来计算线性方程组Ax=b的解使得向后误差算法满足某个优化条件.
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| 关 键 词： | 非对称Lanczos 左右Krylov子空间 向后误差范数 广义拟最小向后误差 |
A GENERALIZED QUASI-MINIMAL BACKWARD ERROR (GQMBACK) ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS |
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| Wei Hongxia.A GENERALIZED QUASI-MINIMAL BACKWARD ERROR (GQMBACK) ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS[J].Transactions of Nanjing University of Aeronautics & Astronautics,2000,17(2). |
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| Authors: | Wei Hongxia |
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| Abstract: | Orthogonal projection methods have been widely used to solve linear systems. Little attention has been given to oblique projection methods, but the class of oblique projection methods is particularly attractive for large nonsymmetric systems. The purpose of this paper is to consider a criterion for judging whether a given approximation is acceptable and present an algorithm which computes an approximate solution to the linear systems Ax=b such that the normwise backward error meets some optimality condition. |
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| Keywords: | nonsymmetric Lanczos right and left Krylov subspace normwise backward error generalized quasi-minimum backward error |
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