加权广义逆、加权最小二乘和约束最小二乘问题 |
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引用本文: | 魏木生,陈果良. 加权广义逆、加权最小二乘和约束最小二乘问题[J]. 计算数学, 1995, 17(2): 196-209 |
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作者姓名: | 魏木生 陈果良 |
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作者单位: | 华东师范大学数学系(魏木生),华东师范大学数学系(陈果良) |
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基金项目: | 国家自然科学基金资助项目 |
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摘 要: | 本文采用如下记号:记C~m×n是具有复数域的m×n长方矩阵的集合,C~m=C~m×1是m维向量的集合.对A∈C~m×n称A~H∈C~m×n是A的共轭转置矩阵,rank(A)表示A的秩,R(A)和N(A)分别为A的值域和零空间,||·||=||·||2和||·||F分别为2-范数和Frobenius范数;I表示恒等矩阵.人们在研究数学规划、数值分析、数据处理,散射理论和电磁学等领域中都将问题归纳为如下的最小二乘问题:
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关 键 词: | 加权 广义逆 最小二乘问题 约束最小二乘 矩阵 |
WEIGHTED GENERALIZED INVERSES, WEIGHTED LEAST SQUARES AND EQUALITY CONSTRAINED LEAST SQUARES PROBLEMS |
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Affiliation: | Wei Mu-sheng Chen Guo-liang (Mathematics Department, East China Normal University) |
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Abstract: | This paper discusses structures and uniqueness conditions ot several differently defined M K-weighted generalized inverses, studies different formulas of the minimum Frobenius norm M K-weighted pseudoinverse, and provides several computational algorithms for computing the minimum norm solutions of the weighted least squares and the equality constrained least squares problems. |
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