| 等式约束刚性加权最小二乘问题的稳定性扰动 |
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| 引用本文： | 魏木生, 张琦. 等式约束刚性加权最小二乘问题的稳定性扰动[J]. 上海师范大学学报(自然科学版), 2009, 38(5): 441-451 |
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| 作者姓名： | 魏木生 张琦 |
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| 作者单位： | 1. 上海师范大学,数理学院上海高校科学计算重点实验室,上海,200234
2. 华东师范大学,数学系,上海,200241 |
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| 基金项目： | 国家自然科学基金，上海市重点学科建设项目 |
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| 摘 要： | 研究等式约束刚性最小二乘问题．证明了对于刚性问题，约束加权广义逆，约束加权投影和等式约束加权最小二乘问题的扰动是稳定的，当且仅当系数矩阵的扰动满足若干秩等条件．
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| 关 键 词： | 约束加权广义逆 约束加权投影 约束加权最小二乘 稳定性扰动 刚性 |
On stable perturbations of the equality constrained stiffly weighted least squares problem |
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| WEI Mu-sheng,ZHANG Qi. On stable perturbations of the equality constrained stiffly weighted least squares problem[J]. Journal of Shanghai Normal University(Natural Sciences), 2009, 38(5): 441-451 |
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| Authors: | WEI Mu-sheng ZHANG Qi |
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| Affiliation: | WEI Mu-sheng1,ZHANG Qi2(1.Scientific Computing Key Laboratory of Shanghai Universities,Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China,2.Department of Mathematics,East China Normal University,Shanghai 200241,China ) |
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| Abstract: | We focus on the equality constrained weighted least squares problem (WLSE), with the weight matrix severally stiff. We show that in this case, perturbations of the constrained weighted pseudo -inverse, the constrained weighted projections,and the WLSE problem are stable, ff and only if perturbations of the coefficient matrix satisfy certain rank preserving conditions. |
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| Keywords: | constrained weighted pseudo-inverse constrained weighted projection constrained weighted least squares stable perturbation stiff |
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