J4 ›› 2009, Vol. 44 ›› Issue (10): 30-35.
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岳强 畅大为
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国家自然科学基金资助项目(60671063)
YUE Jiang, CHANG Da-Wei
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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
关键词: PSD分裂;半收敛;最小二乘解;Moore Penrose广义逆
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
Key words: PSD splitting; Semiconvergent; Least square solution; Moore-Penrose generalized inverse
中图分类号:
岳强 畅大为. 亏秩线性方程组的PSD迭代解法[J]. J4, 2009, 44(10): 30-35.
YUE Jiang, CHANG Da-Wei. Preconditioned simultaneous displacement(PSD) method for rank deficient linear systems[J]. J4, 2009, 44(10): 30-35.
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