| 亏秩线性方程组的PSD迭代解法 |
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| 引用本文： | 岳强,畅大为.亏秩线性方程组的PSD迭代解法[J].山东大学学报(理学版),2009,44(10):30-35. |
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| 作者姓名： | 岳强 畅大为 |
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| 作者单位： | 陕西师范大学数学与信息科学学院，陕西 西安 710062 |
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| 基金项目： | 国家自然科学基金资助项目(60671063) |
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| 摘 要： | 将亏秩线性方程组Ax=b增广为以方阵Â为系数矩阵的4×4块线性方程组Âη=b´,再对A进行次正则PSD分裂,得到PSD迭代法半收敛的一个充要条件。最后给出求方程组Ax=b范数最小的最小二乘解的方法并以实例说明, 其中A∈Cm×n,b∈Cm,b´∈C m+n
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| 关 键 词： | PSD分裂 半收敛 最小二乘解 Moore Penrose广义逆 |
| 收稿时间： | 2009-03-16 |
Preconditioned simultaneous displacement(PSD) method for rank deficient linear systems |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University,Xi an 710062, Shaanxi, China |
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| Abstract: | The rank deficient linear systemÂx=b is augmented to a block 4×4 linear system Âη=b´, where A is a square matrix, then A is split with PSD subproper splitting. The necessary and sufficient condition for the PSD method being semiconvergent is obtained. Finally a method is provided to compute the least square solution of minimal norm to ]Ax=b and exmamples are given to illustrate the process, whereA∈Cm×nb∈Cm,b´∈C m+n |
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| Keywords: | PSD splitting Semiconvergent Least square solution Moore-Penrose generalized inverse |
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